If there is one set in the game that embodies the word "uncounterable", this is probably it. Mewtwo's blazing base 130 Speed and sky-high base 154 Special Attack make it a terrifying sweeper and end-game cleaner. Psystrike allows Mewtwo to take out all sorts of special walls, namely Blissey, Chansey, Ho-Oh, and Kyogre, without needing to waste EVs in Attack, by striking (pun unintended) their weaker Defense. Between Aura Sphere, Ice Beam, and Fire Blast, Mewtwo hits everything that resists Psystrike. Aura Sphere destroys the likes of Tyranitar and Darkrai, while doing a lot of damage to Dialga. Ice Beam brings down Lugia and Giratina, especially physically defensive variants. Fire Blast fries Genesect, Scizor, and Ferrothorn, and is Mewtwo's most powerful option in the sun, OHKOing bulky threats such as Jirachi and Arceus-Steel, as well as Lugia, after Stealth Rock damage. Calm Mind pushes Mewtwo's Special Attack to even higher levels, allowing it to take down walls effectively. It also makes Mewtwo surprisingly resilient on the special side, letting it take attacks such as Draco Meteor from Choice Scarf Palkia. Without Calm Mind, Pokemon such as Lugia, Giratina, and 252/0 Arceus avoid being 2HKOed by its attacks.
As for move selection, Psystrike along with three coverage moves is a fine choice. Four attacks Mewtwo is preferable, since setup opportunities are usually quite limited for it. Calm Mind, however, makes Mewtwo much harder to wall. The best moveset for Calm Mind Mewtwo is Calm Mind, Psystrike, Aura Sphere, and Ice Beam, which retains excellent coverage while hitting Lugia and Giratina, the two bulkiest walls in the tier, for super effective damage. If you can give Mewtwo sun support, Fire Blast should replace Ice Beam due to its power and coverage, especially against Genesect. The only Pokemon that stands a chance of walling Calm Mind Mewtwo in the sun is physically defensive Giratina, who can phaze Mewtwo out with Dragon Tail, but even it risks getting 2HKOed by Psystrike. While Fire Blast Mewtwo is the most potent variant, rain's popularity makes Fire Blast less attractive for teams that don't have sun support.
The moves listed above gives Mewtwo best all-around coverage, but they can be replaced if other moves better fit your team. Recover allows Mewtwo to mitigate some of the heavy residual damage that it tends to take. Grass Knot hits Groudon and Kyogre for super effective damage, in particular OHKOing all Groudon, which Ice Beam can fail to do. Thunder hits Lugia and Kyogre super effectively while hitting most Steel-types hard. Shadow Ball is Mewtwo's strongest attack against Wobbuffet, Lugia, and Arceus-Ghost in the rain, while Flamethrower can be used over Fire Blast if you value accuracy. Blizzard is an inaccurate move, but it does allow Mewtwo to 2HKO Specially Defensive Giratina without a boost after Stealth Rock damage, if you hit. Charge Beam allows Mewtwo to quickly finish off a weakened Pokemon and potentially get a Special Attack boost. Taunt can prevent walls from recovering health and can be used in place of Calm Mind.
The given EV spread maximizes Mewtwo's Speed and Special Attack. 4 Defense EVs are used so Genesect gets a Special Attack boost instead of an Attack boost to minimize U-turn damage. Life Orb is preferred to make Mewtwo as powerful as possible, but other items let Mewtwo set up more Calm Minds. If you are turned off by the recoil, Leftovers can lengthen Mewtwo's lifespan, but the power drop is very significant, losing out on 2HKOs against Giratina, 252/0 Arceus, and Lugia at +1. Like Leftovers, Lum Berry lessens Mewtwo's power, but can allow Mewtwo to set up on status-inflicting Pokemon such as Thunder Wave Ferrothorn. Expert Belt gives Mewtwo conditional power while conserving its Mewtwo's health. Even though it does not boost Psystrike most of the time, Mewtwo's coverage is enough to hit most targets for super effective damage. On the other hand, Mind Plate boosts only Psystrike and not Mewtwo's coverage moves. With Mind Plate, Psystrike is still powerful enough to 2HKO specially defensive Giratina and Latias, and OHKO 252/0 Kyogre after Stealth Rock damage.
The only things that keep Mewtwo in check are Choice Scarf users, priority attacks, residual damage, and its inability to cover all threats with four moves. If Mewtwo lacks Fire Blast, Scizor can checkmate it with Pursuit and U-turn, while Jirachi can take anything it dishes out and paralyze it with Body Slam. Metagross can also do lots of damage in return, while not taking much from Aura Sphere. If Mewtwo lacks Aura Sphere, Tyranitar destroys it with no trouble at all, while Dialga, Arceus-Dark, and Darkrai can be troublesome outside of sunny weather. If Mewtwo forgoes Ice Beam, then Lugia counters Mewtwo without sun, while Giratina becomes a big problem. If Calm Mind is omitted, Mewtwo has a hard time against defensive teams in general, especially those with Latias, Lugia, or Giratina in them.
Most Ubers teams plan to take down Mewtwo via a Choice Scarf user, as few Pokemon can actually wall it. It should be noted that not many Choice Scarf users can actually OHKO a healthy Mewtwo, but Life Orb recoil and entry hazards can put it in KO range. Most Choice Scarf users require at least one round of Life Orb recoil in addition to Stealth Rock damage to OHKO Mewtwo. The exceptions to this are Kyogre (with full HP Water Spout), Modest Reshiram in the sun, Adamant Kyurem-B and Zekrom, Heracross, Victini, and finally Genesect. Genesect in particular is problematic for Mewtwo, since it can deal massive damage to Mewtwo with U-turn, and avoid being locked into an attack that might be advantageous for another sweeper to set up on. Genesect is a nightmare to try and pin down, but some ways to make life difficult for it is to heavily stack on entry hazards, and try to hit it hard on the switch (Psystrike does a lot of damage, while Fire attacks OHKO it). Wobbuffet can remove most Choice Scarf users, with the exception of those just mentioned. Luring out Choice Scarf users with Thunder Wave Kyogre or other Thunder Wave users is a good strategy. Kyogre tends to lure in Choice Scarf Palkia and Zekrom, as well as Latias. If you do have sun support, though, removing Choice Scarf Kyogre is not too difficult with Wobbuffet, as you can sacrifice Groudon to Kyogre to bring in the sun, then use Wobbuffet to trap and remove Kyogre, keeping the rest of the match sunny. Sacrificing Hippowdon or Tyranitar when using a sand team has a similar effect. Reshiram is difficult to deal with if you are using a sun team, but is easy for rain and sand teams to take on. Victini can be trapped and KOed by Tyranitar or other Pursuit users that are not weak to its attacks. Heracross is walled by many Pokemon, such as the Giratina formes and Groudon. Lastly, as previously mentioned, Thunder Wave Kyogre tends to lure in Choice Scarf Palkia and Zekrom, as well as Latias, a wall that gives Mewtwo trouble.
Residual damage has been mentioned, but it should be stressed that Life Orb and entry hazard damage allow priority attacks and Choice Scarf users to pick Mewtwo off. Rapid Spin and Magic Bounce users will mitigate entry hazard damage. For offensive teams that tend to carry Mewtwo, Custap Berry Forretress, Kabutops, and Excadrill are all good offensive Rapid Spin users, while Xatu and Espeon provide Magic Bounce for the team. Wish support from Blissey or Jirachi can help Mewtwo, but is not always necessary.
In terms of offensive pressure and synergy, sometimes it is best to just stack sweepers with good offensive synergy with Mewtwo. Rock Polish Groudon and Landorus-T can set up on Choice Scarf Zekrom; Scizor, Arceus-Steel, and Bisharp can set up on Choice-locked Dragon-type attacks. Latias can set up on Choice Scarf Kyogre, as can Water-resistant Arceus formes. ExtremeKiller Arceus can set up on most Choice Scarf users besides Choice Scarf Terrakion, which cannot defeat Mewtwo. Dual Screen support also benefits Mewtwo, since they prevent most revenge killers from easily KOing Mewtwo. While Wobbuffet does not have particularly good synergy with Mewtwo, it can still Encore setup moves such as Calm Mind, giving Mewtwo a free setup opportunity.