I use the free hand to hold the hemostats with the needle, and hold the suture tail in my teeth or in a second clamp. Some cuts are awkward to get to yourself and you need a little help with the surgeons knot. I got a cut on my left hand washing dishes while camping many years back. There were a lot of cub scout leaders there, but they were all, "No way am I going to watch or help you do THAT". I had my daughter help me put sutures in .... she was about 10. She would not get all squeamish like the boys and adults would. She is a cardiac RN now.
My best suture story was about 30 years ago. I was setting a diamond for another jeweler who was afraid to do this particular job without chipping a very expensive diamond. I was using a graver to cut the gold away from around the stone as I set it, and the graver slipped. It cut a nice straight slit across the index knuckle of my left hand. I put a paper towel over it the stop the bleeding, and opened the drawer for the suture pack. The other jeweler was sitting about ten feet away in an arm chair. While I was chatting with the other guy I put four stitches in my hand. Once all was done, I cleaned the hand off with some alcohol, and got up to throw away the bloody paper towels. As I passed him, he saw the bloody towels and asked what happened. He jumped up and when I told him that the graver had cut me, saying he would take me to the ER. I showed him the freshly stitched hand and said, "No need, I just stitched it up myself while we were talking." ... He fainted, and we had to call 911.