Peppermints can scavenge and live even after aips are gone - they need fed and you should see them eat like you see the fish eat. They also need iodine at NSW levels to molt properly, so if you don't change water or use a low quality reef salt, then they can be short lived. IME, they will not tackle the large ones - you need to knock those back yourself with some kalk or joes juice.
I have a copperband right now that will eat the aips on one side of the tank, but not the other. The peppermints will only go within about 2 feet of their cave/burrow which leaves a few feet of reef where nothing will eat 'em. I don't have a lot, but enough that I have to go injecting kalk.
If you have a FO tank, just about any butterfly will destroy them. Saddleback are cheap and will really do the job.
People sometimes get rid of their fish/shrimp/whatever once the aips are gone. The aips will likely come back. Nothing will eat all of 'em, so just keep your consumer around.