The mewtwo deck is nowhere near invulnerable, in fact, it has a critical weakness: the fact that it has only 1 or 2 pokemon in it.
 
So, how to capitalize on this?
 
The trick is simply that they can only have 1 pokemon powered up (all the energy must go to mewtwo) and its always not gonna have more than 1 energy.  You might ask what if they use an attack, or don't barrier?  You must always have a pokemon out that can attack to prevent this, and attack early and often.  Second, to finish it off, you can use an energy removal when it has but 1 energy on it, so it won't be able to attack the next turn.  However, only use this if you have a pokemon that can deal at least enough to kill the mewtwo in one shot, and more damage is better. (beware evil defenders/potions)  Also, pokemon that remove energy can also work wonders, once you hit it with the initial energy removal to start hitting it.  If they are foolish enough to place another mewtwo, then a gust of wind can bring it into the line of fire (barrier only affects the mewtwo card that used it, so even if another mewtwo switches out, its not affected)  magneton and magnemite can also deal damage to a benched mewtwo, should your opponent be foolish enough to place one.  If they don't?  Then be sure to remove energy so they can't barrier the next turn, then stomp them with a powerful attack.
 
The other thing is, remember that if your opponent has no pokemon in their starting hand, you MAY draw UP TO 2 cards, and they MUST show you their hand.  So, if your opponents hand is all psychic energy, or perhaps there's a trainer (think if that trainer would work in a mewtwo deck) then don't draw any cards (unless your starting hand rrreeeaaallllllyyy sucks) and if their first (and only) pokemon is a mewtwo, don't use any cards that let you draw.  And also be sure to then use any imp oaks to make them gain cards (buy you more time)
 
To conclude, be careful when drawing extra cards at the start, and be certain to include at least 1 energy removal, if not 2 (if your playing a best outta 3 match, then even if the removal gets into your prizes once, it shouldn't happen twice)  And, should you see a mewtwo, waste no time pummeling it.  Use any attacks and any speed that you can, to deal as much damage as possible, so it will be easier to take out.  And never let your foe do anything but barrier, until you crush the mewtwo's.