What would happen if a Roman Pontiff lost his mental competency, due to senile dementia or severe mental illness? Or what if the Pope were in a coma for a time? Is there a way to remove the Pope, so that a new Pope can be elected?

In short, No, the Pope cannot be removed except by death or resignation. But just as God prevents the Pope from failing in faith, from any wickedness that is contrary to the charism of never failing faith, and from grave errors in doctrine and discipline, so also God prevents the Pope from harming the Faith by loss of mental capacity or loss of rationality. God does not permit these things to happen to the Roman Pontiff, unless it happens after he resigns. So either the Pope would resign, as God would provide for his resignation by grace, even by prevenient grace if necessary, or God would prevent the situation in the first place.

IT is not possible to depose a valid Roman Pontiff.

I would like to add a few comments about this wicked faithless article about the Supreme Pontiff. As previously discussed, it is not possible for a Pope to commit sinful acts of a certain type, those contrary to the Faith. So the accusations made in the article, written by Massimo Viglione and praised by schismatic leader Carlo Vigano, are not possible in any Pope. No Pope can intend, desire, plan, or attempt to harm the Faith, the Church, or the path of salvation. Therefore, the article by Viglione is faithless. There is no Catholic faith in that article.