Welcome to ATP. What part of the world are you living in? Must be a warm place to have leaf cutter ants! You can add your location to your profile so it will appear in each post.
Some sort of bait is usually the best way to stop the whole colony. If you just kill the workers you see, the queen keeps on producing more. A bait is taken back to the nest by the workers and kills the queen. You can find it at a garden store or nursery, if you don't have Home Depot or Lowe's near where you live.
Sometimes you need to try a couple of different baits to get the right one. Some ants eat sweet bait, and some like protein bait. Some also change their diet from one to the other during the season.