[Professor S]

Speaking as someone who has gutted and bled animals before (I used to hunt), I can vouche for the fact that bodies do not bleed much after the body is dead.

When you gut a deer, there is virtually no blood because the animal is already dead and the heart is no longer beating.

If you behead someone, you have severed the nervous connection between the brain and heart, so the heart stops. The only blood that would come out would be some of the blood inside the head, which is a small part of the body in comparison. The rest of the blood would sit where is was when the heart stopped beating.

At least thats one way of explaining it.