No. No it can not.
Mewtwo is famed for having a highly diverse movepool, including the majority of Tms and tutor moves, allowing it to perform practically any type of attack. However, it's cousin Mew beats him is this regard, learning every Tm and Tutor move, besides exclusive ones such as Draco Meteor and Blast Burn. Smeargle is the only Pokemon who comes close, learning almost every move able to be learned except for chatter, Chatot's signature move, through the move sketch, which copies the opponents move and makes it part of Smeargle's moveset.
So unfortunately no it can not, but Mewtwo still has a highly respectable movepool.