No pope can be deposed. It is that simple.
On the other hand, if an heretic somehow is elected, the Apostolic Constitution, Ex cuм Apostolatus officio, provides that, should it become necessary to expel the usurper from exercising his ill-gotten powers, the faithful "shall be permitted to request the assistance of the secular arm against these same individuals thus promoted or elevated."
At the time this was promulgated, February 15, 1559, this would mean that we could appeal to the Holy Roman Emperor to forcibly evict the usurper from Rome, arrest him, and punish him according to his crimes in order to place a Catholic upon the Chair of Saint Peter.
Today, in 2013, I know of no secular power to whom the faith can appeal. So, although we all have the legal authority under Ex cuм Apostolatus officio to ignore the current papal claimant with impunity (provided we do so because we recognize him as a usurper, an anti-pope), the Catholic secular authorities have been severed from the Church and the Church from the secular authorities. I believe the Modernists made the separation of Church and State one of their first priorities (even before destroying the Catholic sacraments) in order to protect themselves from even a remote possibility of being forced from office under the authority of the Apostolic Constitution cited.
Perhaps we should appeal to Karl von Habsburg, the living successor to the Holy Roman Empire.