What a species can live without head for several weeks as they have brains located inside their body and they can breathe through trachea the little holes present in their body which are little holes which allows oxygen to flow through spiracles pipe directly through the tissues through a set of tubes instead of blood carrying oxygen throughout the body like that of mammels.That is why they are not dependent on their mouth or wind pipe to breathe.
The body structure of the cockroaches are like that they have no blood pressure
The way mammal has they have just open circulatory system which results in decreasing the chances of uncontrolled bleeding and their seals just by clotting.
Heart of a cockroach is a simple tube with valves which can pumps blood forward and backward through the insect. They have the extraordinary ability to slow down the heart rate or can stop heart for pumping without any harm.
Cockroach can live in a air tight jar for a month with its head being cut off they have their metabolism cool temperature it can live without a head and they also need less water to survive.
Eventually if their cut head is nourished with food for a week it can also respond easily. Thus this fact is quite astounding and extraordinary.