It's an urban legend. From:
http://www.messybeast.com/urbancat.htm

THE HEADLESS CAT HOAX

A photo recently did the rounds of an apparently headless tabby cat held
by a veterinarian sometime in 2000. According to accompanying text, the
cat was found on a roadside in Lynchburg, Virginia, USA by a council
employee whose job was to collect and dispose of corpses animals which
had been run over. Half an hour after picking up the cat's body, he
apparently noticed it was still breathing, albeit with difficulty. A
rasping sound was coming from the cat's severed windpipe. He took it
straight to an emergency vet. The headless cat, named Mags, became a
local celebrity and was nursed back to health with an intravenous diet
and a drinking straw to help her breathe. Mags supposedly survived
because her central nervous took over all autonomic functions in the
absence of the brain. She was adopted by an anonymous person, but was
being studied by medical scientists including "renowned British
veterinarian" Kenneth Hubsteed who wrote a medical book about "Mags the
Amazing Headless Cat."
Sounds phoney? It is. The photo is a fake, with the cat's head digitally
replaced by a section of sweater, giving a fuzzy area at the cat's
shoulders. In higher animals, such as cats and ourselves, the central
nervous system can't take control of functions such as breathing or
temperature regulation. If it could, there would be dozens of French
Guillotine survivors. In addition, if the carotid artery and jugular
vein had been severed, the body would lost all of its blood. Even if
some body functions could be taken over by the central nervous system,
the lack of sensory organs (ears, eyes, nose, whiskers) and cerebrum
(the "thinking" part of the brain) would have meant the animal remained
in a persistent vegetative state, body-alive but brain-dead. Finally,
there is no renowned British vet called Kenneth Hubsteed ... and a
British medical book would never have the word "amazing" in the title;
it would have been called something like "Case of post-decapitation
survival in a domestic cat."
Mags the headless cat is a feline re-write of the famous "Mike the
Headless Chicken". This unfortunate (or fortunate, depending on how you
look at it) chicken survived decapitation because enough of the
hind-brain was left for body systems to function and enough of the
chicken's system is controlled by its hind-brain to make this possible.
Mike's forebrain had gone, so the chicken itself wasn't able to
appreciate its unusual mode of survival.

Megan

                                   

This is a spoof ... National Lampoon material.  LOL