Do mosquitoes mutate

All organisms mutate over evolutionary time scales.

But mosquitoes, like some other insects, also metamorphose between stages of their lives. They hatch from eggs and feed as worm-like larvae, then enter a pupa (cocoon) phase during which they transition to a flying, egg-laying adult (also called an imago). So a mosquito has a different appearance as a larva, a pupa, and an adult.