kelly, I would agree with turbosaurus and amputate. It's much simpler than you think. Very quick and easy.
You'll need a plastic tub in which to do the surgery, an air pump with airstone, small steel scissors, gallon-size plastic bags and the clove oil.
Add the clove oil at 5 drops/gallon to dechlorinated water in the plastic bags. Seal up the bag and shake vigorously until it is thoroughly mixed. Dump into the tub, and repeat until you have just enough water in the tub to cover your fish. Add the airstone to keep the clove oil in solution.
Sharpen the scissors to ensure they will cut, not tear, his fin. Boil the scissors to sterilize them, then net your fish and put him in the tub. He will swim around for a while, then roll over onto his side. Once his gill movements have slowed and he doesn't wiggle away when you touch him, lift his fin out of the water and clip away the fin just above where it has broken. Leave a nice straight, clean edge so there is no place for fin rot to set in. If you like, you can carefully dry off the edge with a paper towel and smear Neosporin or Bio-bandage on the edge to promote healing.
While you are doing all this, keep his head underwater and ensure his gills are still moving. If they slow down too much, add some fresh water to dilute the anaesthetic solution in the tub.
Once you are finished, remove the fish to a bucket of clean water. It will take him a few moments to wake up, and he will be a little unsteady. You can hold him and move him gently back and forth in the bucket to swish water over his gills and speed his recovery. Once he can swim on his own, return him to the tank.
It's a super simple surgery, really, and will help prevent fin rot or infection from setting in. He will heal much faster if you do the surgery, and you will probably prevent a lot of pain. It would hurt him much less to have the fin amputated and healing than to have the injured fin flopping around.