Can Mewtwo learn any HM moves?

Only some HMs, such as Rock Smash, Rock Climb, and Strength.

It can't learn Surf, Waterfall, Cut, Whirlpool, or Fly.

Why: Surf (Not a water-type) Waterfall, (Same Reason) Whirlpool, (still!) Fly (IT DOESN'T HAVE WINGS!)