Zeds arn’t literally corpses though. I mean ff they were biologically dead they couldn’t move, first due to rigor mortis (brought about by a lack of ATP to return lost ions to the muscle cells and reset actin/myosin fibers) and secondly as the fibers themselves turn to mush with lactic acid build up and accelerating bacterial action.
Now, that doesn’t mean they necessarily should NEED blood pressure anymore, but that doesn’t mean they don’t either.
Given the fluid nature of the contagion and how the blob seems favor hydraulic power to move in its isolated/pure forms it seems likely that the blob would try to maintain a fluid seal it it’s current host (at the very least to continue preserving nutrition for growth and energy.)
Then again, cutting weapons have been called a bit OP before… even I don’t particularly favor them.