I use to catch them every once in a while out catfishing.  I would either get the hook out with pliers or cut the line.  I don't want to leave my hand near a snappers mouth any longer than necessary.

Growing up on a farm we had/have a creek which meanders through a cow pasture behind our farmhouse.  If we found a snapping turtle, having great respect for those powerful jaws, my brother and I would spend hours trying to capture it.  Who needs a computer or smart phone when you have THAT kind of entertainment?!  (Incidentally, we would always let the turtles go afterwards). I guess having been exposed to that kind of thing gives me a different perspective.  Don't get me wrong, I don't want to cozy up to one in bed or have one over for drinks but I think they are pretty cool.

 

Fly fishing a few summers back I was catching small bluegill (lots of stunted fish) and a big old snapping turtle rose to the surface a few yards out in front of me.  I began swinging the fish over to the turtle where he had himself a lovely feast.  I know it probably wasn't wise as now sen'ior turtle probably associates people with his (her?) next meal but I couldn't help myself.

 

I rarely, if ever, use live bait so catching turles on a hook and line hasn't happened (yet).

Turtle are very good eating....Hate to say it, but, kinda like chicken, no wild or gamey flavor....Your missing out if you haven't tried it .....Better than many other wild game .

I have caught snappers before. Its cool to hear them hissing like cats. but I usually try to pick them up by the shell and remove the hook and bait. Let it go. I usually get them in 20 pounders and sometimes 30s. They can get big here. I've noticed they like pork scented lures like Net Bait.