Bugs have more primitive systems then we do, so yes, cutting off their heads will leave them still alive for several minutes to several months depending on what bug you're talking about.Have you noticed how crickets always struggle, even if they are half eaten by a mantis? They have primitive minds. The only thing they think is to eat, survive, breed. No bug wants to die, they would probably rather a slow death then a forced one. They want to live no matter what happens to them, it's just the way that the natural bug instinct works. At least, in my opinion that is the way it works. And in nature, there isn't a 'quick-and-painless' way of dying for a crippled mantis.