Whether a heretical pope can be deposed is actually one the many many debatable issues in R. Catholicism. The problem is that while a pope may be said to be “ipso facto” deposed in the light of manifest formal heresy, yet since he is above all councils then he cannot be formally deposed by them without his consent. Thus you have both yes and no answers.
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The Councils of Constance and of Basle affirmed with great emphasis that an Ecumenical council is superior in authority to the pope, and French theologians have adopted that proposition as one of the famous four Gallican Liberties. Other theologians affirmed, and still affirm, that the pope is above any general council...
By taking our stand on the Scriptural doctrine that the Church is the mystical body of Christ of which the pope is the visible head, we see at once that a council apart from the pope is but a lifeless trunk, a "rump parliament", no matter how well attended it be.
Can a council depose the pope?
This question is a legitimate one, for in the history of the Church circumstances have arisen in which several pretenders contended for papal authority and councils were called upon to remove certain claimants. The Councils of Constance and Basle, and Gallican theologians, hold that a council may depose a pope on two main grounds:
ob mores (for his conduct or behaviour, e.g. his resistance to the synod)
ob fidem (on account of his faith or rather want of faith, i.e. heresy).
In point of fact, however, heresy is the only legitimate ground. For a heretical pope has ceased to be a member of the Church, and cannot, therefore, be its head. A sinful pope, on the other hand, remains a member of the (visible) Church and is to be treated as a sinful, unjust ruler for whom we must pray, but from whom we may not withdraw our obedience. - http://www.newadvent.org/cathen/04423f.htm
Cardinal Cajetan, a noted Thomist theologian in his field, felt there could be a heretic pope. But no man may judge the First See. How does he reconcile this?
St Robert Bellarmine again explains:
"Besides that, the second affirmation of Cajetan, that the Pope heretic can be truly and authoritatively deposed by the Church, is no less false than the first. For if the Church deposes the Pope against his will it is certainly above the Pope; however, Cajetan himself defends, in the same treatise, the contrary of this. Cajetan responds that the Church, in deposing the Pope, does not have authority over the Pope, but only over the link that unites the person to the pontificate. In the same way that the Church in uniting the pontificate to such a person, is not, because of this, above the Pontiff, so also the Church can separate the pontificate from such a person in case of heresy, without saying that it is above the Pope."
St. Robert than refutes this, however, with his own response, basing it on the Fathers:
"But contrary to this it must be observed in the first place that, from the fact that the Pope deposes bishops, it is deduced that the Pope is above all the bishops, though the Pope on deposing a bishop does not destroy the episcopal jurisdiction, but only separates it from that person. In the second place, to depose anyone from the pontificate against the will of the deposed, is without doubt punishing him; however, to punish is proper to a superior or to a judge. In the third place, given that according to Cajetan and the other Thomists, in reality the whole and the parts taken as a whole are the same thing, he who has authority over the parts taken as a whole, being able to separate them one from another, has also authority over the whole itself which is constituted by those parts." http://forums.catholic.com/showpost.php?p=5273453&postcount=11 Of course, since in the record of the NT church in Scripture, there was no perpetual infallible manifest papal office in Rome to which the church looked as such,then there is none to depose.
Church structure in the NT was much simpler as per Paul in his letters to Timothy and Titus.
Elders and deacons for local church bodies.
For all the convoluted mess the Catholic church has become, God did not make it so complicated.
Not only that, I see NO mention of God or the Holy Spirit being involved in the process of either electing the pope or removing him from office. Seems that the Catholic church hierarchy is perfectly capable of running without input from God.