Why does a cockroach not die even after decapitation?
Based on an article here, unlike humans, cockroaches have an open circulatory system. They don't have a huge network of blood vessels like that of humans, or tiny capillaries that you need a lot of pressure to flow blood through. Hence after you cut their heads off, very often their necks would seal off just by clotting.

According to the article cockroaches breathe through spiracles, or little holes in each body segment. Plus, the roach brain does not control this breathing and blood does not carry oxygen throughout the body. Rather, the spiracles pipe air directly to tissues through a set of tubes called tracheae. In addition cockroaches are poikilotherms, or cold-blooded, meaning they need much less food than humans do. Hence cockroaches can survive decapitation.