A cockroach can survive for about a week without its head

A decapitated cockroach can stand, walk, and respond to touch for about a week before dying — not from the wound, but from thirst. The reason lies in an open circulatory system and body-wide breathing that make the head, biologically speaking, almost optional.

Source: A cockroach can survive for about a week without its head, dying eventually of thirst rather than injury, because its open circulatory system and body-wide breathing let it function long after decapitation would kill a mammal