It seems attempting to counter Monastery Mentor the card isn't the approach to take, as poignantly demonstrated by Brassman's initial play-in for this season's VSL: playing anti-mentor.dec against a gauntlet of THREE mentor decks and going 1-2. I'm sure there are arguments to be made for variance and other factors, but it was tough for me to swallow a deck running maindeck Sulfur Elementals and massive amounts of removal to have so little of an effect.
Right now, the most efficient answer to Monastery Mentor the card seems to be attacking Monastery Mentor the deck. That is, if you're comboing or using mana denial to marginalize their strategy, you can stay ahead of the card's raw efficiency. Currently "silver bullets" don't work.