According to bulbapedia, it has only showed up in Pokemon Origins when cut was given to red by the Captain of the S.S. Anne.
Other than that, nothing else in the anime.
The manga had Red having a bunch of HMs, namely Cut, Strength and Flash. Misty's krabby had surf. Blue had surf before red. In Pokemon Zensho, Satoshi got the Cut HM from the captain of the S.S. Anne
Hope this helped!