I think it's one of those things where a lightsabre is only on if the user has his/her finger on the activation button. Thus, once one takes their finger off the button, it automatically deactivates (or in this case, their entire hand).

Granted, in JEDI Vader throws his lightsabre at Luke up on the walkway and the sabre stays activated when it knocks the walkway down (and Luke with it). One can say that a Force user can use the Force to keep the button pressed down to allow the throwing of an active lightsabre, but that would require at least a small bit of concentration. When one is getting their hand chopped off, it's probably a bit hard to concentrate on anything.