Chris Beam answers:
No.
The Code of Canon Law has no provision that allows a pope's removal from office for any reason, even poor health or psychological trauma. That's because, according to church law, there is no higher authority than the pope: He "possesses supreme, full, immediate, and universal ordinary power in the Church, which he is always able to exercise freely." A pope may resign, but his resignation must be "made freely," and he doesn't have to tender his resignation to any particular authority. (The last pope to resign was Gregory XII, who did so in 1415 to end the battle for the papacy known as the Western schism.)
2006-2011 archives for The Daily Dish, featuring Andrew Sullivan