>>26791814The fact that Mew can learn all of the TMs/HMs were an oversight due to the hasty inclusion of Mew in RGBY (added the fact that It can learn transform and metronome on its own); once Game Freak got wind of it, they decided to canonize that oversight in future games (like how they canonize the Nidorina/Nidoqueen can't breed glitch in GSC).
So yeah, it can learn Crab-hammer when Move Tutor offer to teach it, but that depends entirely on the move tutor (like how they refuse to teach it starter beam and Dragon Meteor).