We see in Guardians of the galaxy that he can have his arms servered, shot at and blown up. So can Groot be killed in the Marvel cinematic universe?
Groot was almost completely destroyed in the film.
Rocket had to replant a splinter of him in order for him to regrow.
Therefore, if you destroyed every single piece of him, he'd probably be dead for good.
Additionally, the Collector believes that Groot can die.
The Collector: I never thought I'd meet a Groot. Sir, you must allow me to pay you now so that I may own your carcass. At the moment of your death, of course.
I don't see why not.
Groot is the last of his kind, which presumes that his species was eradicated somehow. I'm not sure if his being the last of his kind is mentioned in the movie so....if we just suppose that he is only an animated plant, he would need water (seen in the movie drinking) and perhaps some other form of nutrient (never seen eating anything else although he does have a mouth), and light.
I don't see why he would be able to survive if placed in a de-humidified room without water, nutrient, or light. If you wanted to be certain, (as some drought resistant plants can be revitalized with water after completely drying out) you could always burn the remains.
Perhaps something as simple as an herbicide might work...
His body reacts like most plants, regrowing, producing many offspring, etc.. Like with a tree, the loss of a branch should not cause death. Inhabitable conditions, however could result in failure of bodily functions and death. Also, lack of a food supply or water could kill the plant-like being.
According to the Guardians cartoon that came after the first movie.
In the Groot origins episode as long as Groot is alive there is hope for his entire species.
Dont know what kind of canon this falls under but the cartoons are still being produced and I guess they will tie in with the next movie somehow.