I'm not quite sure about this. Oxygen deprivation, like the kind that would be caused by a lack of circulation, causes dizziness and not pain, and massive trauma has been known to cause numbness rather than intense, searing pain. If you did feel the pain, you would probably pass out rather than experience the agony due to the trauma of the experience, dying relatively painlessly.
EDIT: I also wish to note that if I did have to die, I would definitely choose death by Guillotine over the Electric Chair or the Lethal Injection. Aside from being (probably) less painful, it would be a better spectacle, and my family would get a neat decoration if they chose to keep my skull.