I think you failed at some way because the only way you get cut is in and not directly after the 2nd gym. Or did I missunderstood you and you got it not directly after the 2nd gym?
In the game the leader of the second gym tells you to get the cut TM from the person at the front of the gym, which I bought from the person for $1,500. It was in my bag ready to be used I just didn't put it on any of my pokemon. I went back on the next day and it wasn't there. I can't progress to Saffron City if I don't have it.