The remixed version of the Elite Four still exists for Mewtwo to be used against. But, yeah... he's basically Athos 2.0 as far as tiering goes.
Ice Beam isn't one per game, which makes it more reasonable than stuff like Earthquake or Rock Slide, though it's still not almost-free like Brick Break. You should be able to afford two boltbeam tier TMs from the Game Corner if you fight the majority of trainers in-game, more if you prioritize getting the Amulet Coin. Last run through I managed to buy 2xThunderbolt, 1xIce Beam, 1xShadow Ball before the E4 even, and I didn't touch slots at all.