As someone who made the mistake of watching one of the beheadings online, trust me that you do not want to see that. I suffered what could be best described as PTSD for a few months after witnessing that. Not only do I not want to remember what the severed head did, I don't want to remember anything about watching that video.
As far as the hypothetical nature of maintaing a severed head, I think this would be techniccally feasible if a few criteria were met.
(1) You would have to bypass the carotid and jugular venous returns sequentially. Having seen many carotid endarterectomies performed where the internal carotid artery is cross-clamped and subsequently bypassed to the patients own circulation via the external jugular (because of lack of sufficient contralateral patency to perfuse the brain), this would be technically feasible.
(2) You cannot discount the aerodigestive tract in maintaining normal function of the head. Not only does this serve to a small extent in cooling, it also serves to keep the sinuses clear of secretions, which are a nidus for infection. In long-term ventilated patients, where the sinuses are bypassed by an endotracheal tube, this can be problematic.
(3) The function of the lymphatic system would have to be maintained. Even though you have lymph nodes in your neck, these all eventually drain through the thoracic duct into the central circulation. Disruption of this system would lead to massive lymphedema of the head, unless some mechanism was instituted to also bypass the normal evacuation of this system.
(4) There would have to be some sort of reticuloendothelial system in place that would help in the normal day-to-day regulation and turn-over of dead cells and proteins. While the cervical spine, if left mostly intact, could contribute to this, the bulk of these cells - namely macrophages - come from the hematopoetic system located in the thoracic and lumbar spine, large bones (such as the femur), the liver, the spleen (which serves as a reservoir), and the bony rib cage. Developing an "artificial" system for this - barring the potential for infection - would be difficult, and wrought with rejection issues if some surrogate was found.
(5) I'm sure there are other things I can't think of right now that would preclude a longterm survival of such a scenario.
The point is, the animal/mammal body is an entire system that has evolved over millions and millions of years. Isolating a single part would be complicated, even given the best of medical science. And, it certainly would be expensive. If you consider that even just a stay - just for the bed - in an ICU averages about $4000 a day... then you've got to add-in the bypass equipment, the changing of fluids, etc., etc. Not to mention that we are not at the state where we can accurately and reliably synthesize the human immune system in vitro.
The best bet would be to transplant the head onto another body, as others have said, and it would have to be a one - like in the identical twin - where major histocompatibility is assured, otherwise you'd be equally fraught with rejection issues. And, remember, even in twins there are different environmental exposures to antigens and development of diseases.
Not an easy task, anyway you slice it...
-Dr. Imago
Somewheres, they just transplanted a human hand. I would feel real weird wearing someone elses hand, let alone their entire body. I don't think my mind could cope.