I do not snag the bottom very often, but when I do, I immediately spin the boat (if I am by myself) to the side of the downrigger I am using and run a course 180 degress back over the spot. 9 times out of 10 this frees the ball.
Not to mention, I had the plastic clip break more times than I have had to cut the wire. I never try and pull it free. That's too much stress on the boat. If I have two riggers in, I just throw the boat in reverse. I would rather have the fishing line wrapped on the wires than the wire(s) caught in the prop any day.

The Scotty's have a clutch system which allows for the line to pay out if you snag. This is a great feature... especially when I am not paying any attention....

Some folks swear by the heavy green snubber.
I personally do not like because the clips are inadequate and a pain. Plus I like the "feel" of a straight wire/ball connection.

The only time you can really worry about snagging the bottom is when you are fishing into ledges or fast dropping/ascending depressions on the bottom. However, you never know what's down there!

Lastly, avoid fishing fast and strong currents while downrigging... This could spell BIG TROBLE if you snag up. If fishing in strong currents is unavoidable, make sure you have the wire cutters sharp and handy- don't delay!

Downriggin'