I don't think M2 really loses to sword characters, for example, because it has a lot of ground speed, tricky aerial setups, and enough disjointed range on certain normals to take advantage of holes, but if what you mainly remember are the times Mewtwo gets juggled, or the times Mewtwo dies at a low percent to a rogue F-Smash, then it's going to seem like Mewtwo is at a disadvantage when I don't think it really is.
FWIW I think Mewtwo beats Link. Unlike the other swordsmen Link relies on projectiles a lot, so reflectors put a kink in his major plan. Link's disjoints are also weaker from the sides in air-to-air, since bair and nair have no disjoint and fair's is lesser than Mewtwo's bair. Link would only air approach from vertical directions but since Link doesn't fly well, horizontal air approaches happen more often. On the ground Mewtwo's dtilt and Shadow Ball ensures Link's disjoints don't own the road. So, on-stage, I think the MU is evenish, but if the match gets sloppy Link of course pulls ahead. It's the off-stage game that's the dealbreaker. Mewtwo gimps Link easily, Link can't reply in kind. And Link's best anti-gimping tactic of tossing a boomerang at the ledge he's chasing works against him as well, since Mewtwo can reflect it en-route, giving Link 2 problems instead of one. I don't even see Link's customs improving the MU much if any. Mewtwo can't mess up obviously, but MU ratios presume no appreciable mistakes happen.
Not that having a winning MU against a Hyrule-tier hero means much... not even keeping you out of Hyrule tier yourself.
I can see Toon Link having similar issues, though with Mewtwo having a bit more leeway in messing up. But Toon Link's mobility make messing up a bit more likely, so that's a wash.
On the flip side, I can't see Marth having any problems with Mewtwo. Nothing to reflect, Disable has less range than the sword, and tipper even kills heavies at ridiculous percents.