I feel conflicted because I play both Mewtwo and Link.
Anyways:
Mewtwo's aerial mobility thanks to his double jumps and range with midair Confusion (gives him some slight horizontal movement in the air) + Teleport means that he can go deep after Link offstage.
Which causes all sorts of problems due to the fact that as we all know Link's recovery is quite predictable.
Confusion poses a problem because Mewtwo can nonchalantly reflect Link's projectiles. And as some have mentioned, Mewtwo has options out of Dtilt to deal serious damage, Fair, Nair, and at a little higher percent, Uair, are all true options which can build percent quickly.
I have not tested it yet, but I do worry that idle Hylian Shield will have problems blocking Shadow Ball due to the fact that Shadow Ball follows an oscillatory path.
Returning to offstage, Mewtwo's Nair can be an obstacle to Zair because it covers his entire body, Mewtwo can just drop between Link and the ledge as he is returning with Zair, Nair, and potentially disrupt the Zair attempt. This is a problem not only because Mewtwo's Nair has some range (because it covers his entire body) but also because the Nair sits out for a long time.
Furthermore, Mewtwo's double jump itself makes it very easy for him to chase with aerials offstage, because it sort of "starts slow" but lifts him very high, Mewtwo can drop low and then DJ -> Fair, Dair, etc and connect as he lifts himself back up.
I can't tell you how many times I've done this and how safe an option it is for Mewtwo offstage, i.e. be very wary if Mewtwo jumps off the ledge.
Thankfully, Mewtwo's moves do have to respect disjointed hitboxes, if he tries to challenge something of Link's on the ground, say F-tilt, Mewtwo will typically lose. In the air, his Bair will also typically lose to any disjoints, it has range, of course, but Mewtwo can still be challenged.