As I understand it, it's not like the caterpillar morphs into a butterfly, the way a tadpole turns into a frog. What happens is that the caterpillar sort of dissolves into a soup of protoplasm which eventually organizes itself into a butterfly. There's basically nothing left of the caterpillar structure.

Whether one considers that a "death" or not is a matter of definition. After all, one could argue that when an animal gets eaten by another one, the prey animal "lives on" in the form of part of the predator.