How long a beheaded cockroach can survive? Scientists say a week or may be more. As it has an open circulatory system and unlike humans, who breath through nose and mouth, it breaths through little holes in the body and is not much depe­ndent on the head. But a headless cockroach dies of thirst because it can’t drink water. Then again, cockroaches are poikilotherms (cold-blooded insects) they need much less food than humans do. Cockro­ac­hes can survive at least 2 weeks without food. Though cockroach­es have two brains, one in head and other in butt, they don’t co­n­trol breathing or oxygen circulation. The spiracles pipe send air directly to tissues through a set of tubes called tracheae.