Either make Cut useful, or relieve it from its role as an HM. I don't really care about anything else.
^this. Good god, you know an attack's pathetic when TACKLE, of all moves, ends up leaving it in the dust after a boost. Seriously, as of gen5, basic beginner move Tackle is essentially Cut with slightly more PP and 100% accuracy (Cut's still at 95%). Considering it's, as its name implies, a slicing move (much like Slash, Leaf Blade, Poison Tail.... at least when Poison Tail was exclusive to Seviper... etc.), it could at least have its critical hit rate upped to make up for the small attack power.
Personally, I wouldn't mind if Cut was given a very small chance of causing an instant KO (all the more sensible given its Japanese name, Iaigiri*). It'd essentially be a one-hit KO move, only it gets to do some form of actual damage even in the event of failing, with the trade-off being an even smaller chance of succeeding (the current one-hit KO moves already being at a meager 30%, and freezing moves have 10%, so anywhere between that and a 1% chance perhaps?). Would it be too broken? Would it still not make it competitively viable? All I know is that it's a form of change that this crappy move desperately needs.
*Iaigiri, or Iai Cut. Iai is basically the art of drawing a sword from its sheathe and re-seathing it after one slice. With one slice being all the user needs, it's often portrayed as an instant-kill move in media. http://en.wikipedia.org/wiki/Iaido
Using Gen V's HMs as a basis, I think Fly, Strength and Surf are fine. Strength is even pretty strong with a normal type for in-game, and once you've pushed the boulders into their pits, they stay like that forever.
Cut is a bad move, the little bushes are pointless obstacles that only block like one item before you even get the HM, and they keep regrowing every time you come back. It shouldn't be a HM.
Waterfall is a good move, but I don't like having half of my HMs being water moves. Surf is pretty much a must, Waterfall I believe we can live without if we wanted that.
I found it annoying that Dive was a HM that only gets used once. It may as well be a TM like Flash.
I'd keep them as they are but allow a Pokemon to learn one or two HMs as non-battle moves. I would also change Cut's type to Grass for no other reason than to make it a viable and readily available mid strength attack for physical grass types.