When the carotid artery gets cut..the blood loss to the brain is immediate and thus you don't get a lot of struggling...the body goes limp very rapidly!
Don't know about humans, but we do a lot of butchering here at home and whenever you cut the neck (or the head off) of a turkey, goat, sheep, chicken they all jerk around. Sometimes it is not at first - like going into shock kind of thing - but after a few seconds they spasm and it is an autonomic response. The body just responds to it that way on it's own. That said, I believe that Berg was dead when they cut his head off AND it doesn't make one whit of a difference whether or not he was dead. Doesn't make it less horrific nor does it make it President Bush's fault - only the subhuman evil-doers.