Terminator 2 was still an R-Rated film...Cameron knew it would be well before he finished editing it, and so he didn't have to kowtow to a wider audience if he didn't want to.

The thing is, both Terminators were equally singular in their missions, it's just that the second one had the disadvantage of being hamstrung. Before that, and even after, you'll recall his favor of strong-arm tactics, he broke a cop's arm, and shot him in the leg, he kicked the filling out of a whole barful of bikers, and then at the Cyberdyne building shot and/or gassed a bunch of cops.

Besides, the graphic violence in Terminator 2 was a hell of a lot worse than the stuff in the first one.

Not to mention that even IF the right hand was cut off, how the hell would he push the buttons to activate the self destruct on his other hand?