There are several possible approaches to refuting this viewpoint, but I would just like to zero in on just one of them. It involves the incontrovertible fact that plants needed to cease living in order to support animal life, according to Genesis 1:29-30.
“No-Death” proponents try to get around this difficulty by claiming that the death of a plant or invertebrate is quite different from the death of a “living” or “soulish” (nephesh) creature such as a vertebrate or human being. Their reasoning is two-fold: (1) Only the latter are said to be “living” beings and (2) It is never stated in the Bible that plants and invertebrates “die” (mwt), at least in not at all the same sense that “living” creatures die. For example, plants are said to wither (yabesh) instead.
Both of these contentions are wide open to the charge of being mere speculation if either (a) any scriptural references can be shown to include plants and invertebrates in the category of “living” beings or (b) there are any passages stating that plants or invertebrates die, using mwt, the same Hebrew word employed for vertebrate deaths. Here are some passages that may be pertinent in that respect, listed in the order in which they appear in the Bible.
Genesis 1:24-25
On the sixth day of Creation, God said, “Let the earth bring forth living creatures of every kind.” and then he enumerates the sub-categories of these “living creatures” as (1) cattle, (2) creeping things and (3) wild animals. The question at this point is: What constitutes creeping things?
Wenham says that it “refers to mice, reptiles, insects, and any other little creature that keep close to the ground.” Thus, clearly invertebrate land creatures are considered to be “living (nephesh) creatures.”
Genesis 6:17
A similar point arises in this passage regarding who or what will die in the Flood. The text says that the deaths will include “all flesh in which is the breath of life; everything that is on the earth shall die.” So even if it is said that plants do not breathe oxygen like animals do, the second explanatory phrase in v. 17 seems to indicate that this same “death” apparently includes invertebrates as well as vertebrates.
Genesis 7:22-23
We get a little further clarification in verse 22 as to the identity of “all flesh.” It is said to include birds, domestic animals, wild animals, all swarming creatures that swarm on the earth, and all human beings, “everything on dry land in whose nostrils was the breath of life.” And then in verse 23 the category of “creeping things” is added.
In this passage, we are introduced to another class of animals subsumed under the category of “all flesh” and “everything on earth which breathes.” That is the group of swarming (srs) creatures. According to Hill, “seres identifies primarily swarming aquatic creatures and insects.” Similarly, Wenham says that it includes more than just insects, but “they are small creatures that often occur in swarms and move to and fro in haphazard fashion. 'Swarmers' are to be found on land, in the sea, and in the air.”
Genesis 8:21-22
Finally, in this passage we see that those destroyed were “every living creature.” And we are even given a hint that the death of plants occurred during the Flood when God promises never again to disrupt the cycle of plant life.
Exodus 10:17
Following the plague of locust which left nothing green in the land of Egypt “no tree, no plant in the field,” Pharaoh says to Moses, “Do forgive my sin just this once, and pray to the LORD your God that at the least he remove this deadly thing [literally 'this death'] from me.” That could possibly refer to the death of plants, but other explanations are much more likely, as seen below:
Propp says, “Pharaoh speaks as if he alone were suffering in contrast with his previous mention of himself and his people (8:4; 9:27)...Pharaoh's overstatement proves prophetic. He does not suspect the true death about to strike Egypt.”
Knight: “Egypt is now left to starve...No wonder then that Pharaoh refers to the event as 'this death.'”
“Durham: “Pharaoh indeed has not been in such straits before. Not even had the terrible destruction of the hailstorm...stirred in him such panic, for once ended, the hailstorm left hope amidst destruction in the living men, animals, and crops. These locusts, however, were systematically and thoroughly cutting off Egypt's future. The only word for it is Pharaoh's chilling description: 'this death' a still further echo of the frightening prospect brought by the worst of the mighty acts to this point.”
Thus, we see that it is not just the fact that the plants had “died,” but that it meant “death” for all of Egypt.
Leviticus 11:10-11
After describing the clean animals of the sea which have fins and scales, this law says that “anything in the seas or the streams that does not have fins and scales, of the swarming creatures in the waters and among all the other living creatures that are in the waters – they are detestable to you.” Thus, the invertebrate shellfish, squids, octopi, etc. are also considered as “living creatures.”
Job 8:11-13
After giving examples of plants withering, Bildad concludes, “Such are the paths of all who forget God.” So even if mwt is not applied to plants here, “wither” (yabesh) is applied to both human beings and plants here in reference to their common deaths.
Job 12:7-10
Job mentions the animals, plants, birds and fish and then lumps them all together as “every living [chai] thing.” In this case, a different Hebrew word is employed for “living,” but one that is used throughout the OT to describe God, human beings, and vertebrates.
Job 14:8
Job says that a tree will be cut down and its stump die (mwt) in the ground.
Ecclesiastes 10:1
“Dead flies make the perfumer's ointment give off a foul odor.” Thus, we are taught that apparently insects can die. But Longman points out, “Numerous issues surround the translation of dead flies (zebube mawet)...the Hebrew most naturally means 'flies of death,' indicating either 'poisonous flies'...or perhaps 'doomed flies'...Perhaps it is best simply to take the construct as attributing death to the flies.”
Isaiah 51:6
“Those who live on it [i.e. the earth] will die [mwt] like gnats.” In other words, insects and human beings die in the same manner.
Isaiah 66:24
If the worms who devour the damned never die [mwt], that may mean that the damned will suffer everlasting punishment and/or the worms will have such an ever-renewing source of the damned that they will live forever. In this context, it certainly does not merely state that no worm is capable of dying [mwt] but infers just the opposite.
Jonah 4:6-7
In this passage, God first appoints a plant to grow up and provide shelter for Jonah, and then he appoints a worm to eat up a plant. It is difficult to explain how supposedly soul-less creatures could have the ability to obey a command of God.
As we move on to NT passages, we might expect some further revelations as to what sort of life and death living things possess. But we must remember that the language here is Greek, not Hebrew, and so it may not be possible to make a direct statement regarding life and death before the Fall.
Luke 3:8
Jesus makes the outstanding proclamation in this verse that God is able to raise up children of Abraham even from non-living stones. This should certainly warn us against making any hard and fast statements regarding what is living, what is non-life, and what is dead. Apparently God's definitions are a bit broader than our narrow understanding.
Luke 4:3
Similarly, if Satan is correct in his understanding here, God is able to transcend the categories of the non-living and plant life by turning rocks into bread. And Jesus appears to agree with this understanding, although he doesn't fall for Satan's trap.
Luke 19:40
“Living” stones even show up a third time as Jesus is entering Jerusalem. As the multitudes praise Jesus in joyous welcome, he makes the comment to the critical Pharisees, “I tell you, if these were silent, the stones would shout out.” Of course, we can dismiss this as mere hyperbole, but it may possibly indicate that even inorganic matter is “alive” enough to respond to God in some manner or another.
John 12:24
In this interesting discussion, Jesus attempts to explain the necessity for His upcoming death. He uses the analogy of plant life and death when he says, “unless a grain of wheat falls into the earth and dies, it remains just a single grain; but if it dies, it bears much fruit.” That does not constitute any sort of absolute proof that plants die in the exact manner of human deaths, but we may take it as again indicative of the biblical propensity to equate the two throughout both Testaments.
James 1:10-11
James avers that the rich man will “wither” and “fade away” like the flower. This is contrary to the idea that only plants can wither; the same verb is used to describe the death of a plant and a man.
Jude 12
The author compares those who reject divine authority as “autumn trees without fruit, twice dead, uprooted.” The analogy again equates the death of human beings with the “death” of plants, trees in this case.
Revelation 8:9
In this plague, “a third of the living creatures in the sea died.” So here we see the recurrence of the OT phrase “living creatures” as well as the verb “die” applied to everything living in the sea, presumably including the many invertebrate animals there and possibly the plant life as well.
Conclusion
In summary, we can now say why the following comments can be safely made with plenty of scriptural support:
“As a result of God's creative activity, both animals and people are 'living creatures.' In this sense, all of animate nature is on similar standing.” (Brensinger)
“mwt ['die'] occurs hundreds of times with the notion of natural death whether of humans, animals, or plants.” (Merrill)
“The literal properties of plants as being alive, growing and fruitful make them a chief source of metaphors and similes for human life...The same qualities that make plants images of life also make them images of mutability. If plants can grow...they can also decline. If they live, they also die. No source of imagery for transience is more frequently used by biblical writers than plants.” (Dictionary of Biblical Imagery, p. 650)
Thus, there is no scriptural basis whatsoever for declaring that only vertebrates can truly be considered to live and die.