A friend of mine cuts with her right or left hand. She teaches quilting, and can't be running to the far side of the table to do cutting in front of students.
I have tried cutting with my left hand, using only fabric that is not so important. If I make a mistake on that, I won't care. Trouble is, I don't have enough opportunities to do the practicing, and I am still afraid to try it on my good stuff. Also sometimes I'm just lazy. It's so much easier to just do it with my right hand.