It's derived from French "côtelette", literally "little rib". It's etymologically related to "coast", actually. It being spelled "cutlet" is probably the result of a phonetic spelling of "côtelette" in English being reanalyzed as "cut-let", though, since "a cut of meat" is itself a thing.

It originally referred to the same thing "chop" does today, a slice of meat perpendicular to the spine, containing a single rib. Then it started referring specifically to a boneless chop. Then it started being used to refer to any thin slice of meat. And in a lot of the world it was introduced specifically as a breaded and fried thin slice of meat. And that's how we got katsu, the Japanese version of schnitzel.

Language is weird, isn't it?

Very possible that cutlet means small cut. I don't know the etymology of that word. I was just commenting on the etymology of かつ