You ask quite an interesting question. First, though, you can't be completely decapitated and still have vital signs, although virtually all of the head can be removed but leaving the medulla, which would control (mostly) the autonomic functions. That would be like a little stump on top of the neck, but the rest of the gourd being gone.
The ethical question then arises. It is acknowledged that it is the brain, and not the heart, that makes us people. Moreover, losing the cerebrum is incompatible with life. When someone is declared "brain dead", that is when the head is intact, and the person appears a whole person (even though not responsive). Very frequently, once the determination of brain death is made, the life support systems (like the ventilator) will be disconnected, allowing the body to die. Keeping those people on the ventilator to buy time until the organs can be harvested is a well-known and accepted situation.
So, what becomes of such a body? It still has vital signs, but most certainly has ceased being a person (still human, yes, but not a person). Therefore, where does it stand? If it is not a person, are you actually "keeping it alive"? What is it, exactly, that you are keeping alive? I have training and some small specialization in ethics, so I know what I would do. The next of kin would be contacted. Even if the body has been dismembered, the memory of the person is maintained, and the question of donation can be much more easily addressed, as, in this case, there is absolutely no possibility in any regard, even accounting for the supernatural and unknown, of a "miraculous" recovery, or any other, more tangible, recovery. Immutable and unavoidable. The question of removing life support will occur soon, irrespective of harvesting organs and tissues. If there is no next of kin, the hospital can obtain an ethics consult (and I believe would come to the same conclusions as I have). There would still be brain death testing, which would, prima facie, be concluded as brain death being present (due to the absence of all the structures which would be tested - ipso facto, those are dead). Then, evaluation of suitability for organ donation would occur. The balance of the dignity of the patient, likelihood of recovery, and prognosis would be balanced against premortem wishes and the greater good of organs for transplantation. My interpretation is that the equation tips strongly towards the greater good, and away from the dignity and prognosis. However, if the patient or next of kin made or makes known a specific desire for organs to not be used, and/or to "do everything", that would lead directly to "pulling the plug", as everything had been done. The head is gone, and that person is gone save for memories.
