well think about it ... a dead guy when cut open isnt going to have warm blood start pumping out ... i'm sure a dead person when cut would bleed, but its going to be minimal as in whatever was in the local region when he died
you cut a living person and it continues to bleed until the wound clots, warm pumping blood would be pushed out.
gravity is going to push the blood down ... so you should have very minimal blood when cutting the top side of someone.