quote castlewars
This isn't possible. You need Cut to advance through the game, when you go and get the Dream Mist. Dumping HM slaves won't allow the game to advance.
You can just catch other Pokemon that can learn Cut. And really, the only HM that's used constantly throughout any game is Surf, and just about every water type can learn that. I never use HM slaves and I get through the game just fine.
But anyway, sounds fun. But then again, my Nuzlockes have me dump half my team after each major battle anyway, so it's not all that different from what I'm doing now. Eh
Kanon?