No
HM moves, unfortunately, cannot be forgotten by replacing them with another HM move. In Pokemon Emerald there are only two ways to make your Pokemon forget an HM.
Either:
- The move deleter, who can help your Pokemon forget any of its moves, even if they were taught via TM or HM (excluding Surf under certain conditions)
or:
- The Pokemon Daycare, by making the undesired HM move the first move in the Pokemon's moveslot and then leaving the Pokemon in the Daycare until it learns a new move
I don't recommend trying the Daycare method, as it can be a little frustrating waiting near the Daycare long enough until you're Pokemon forgets the HM move. If you really want your Combusken to forget Cut, you should keep playing until you make it to Lilycove City, where the move deleter lives. There are plenty of oppurtunities for you to obtain hidden items with Cut until you get there though, so try to make the most of it!
Coming from a player who knows from experience just how annoying HMs can be.
Source
Good luck with your playthrough!
