Mark Shea says no, he can’t. Interesting, his explanation for why not:

The irony, particularly in Dreher’s case, is that in his frustration and sense of crisis about the Roman Church, he chose to be jump to the ecclesial camp which would be most irate if the Pope did was Dreher demands. They, better than I, can explain why the Pope is about a thousand years to late to go all Innocent III on us and imagine that it is his role to effectively take over the management of every diocese in the world and expel a huge number of bishops from their sees, not only for being fools when it came to the culture of secrecy in the abuse scandals, but for all sorts of other reasons as well.
T’aint gonna happen. (Not that I don’t wish it would some days. I long for the expulsion of toads like Mahony from their sees.) But the reality is that this Pope appears to be pursuing almost exactly the same course as JPII when it comes to dealing with idiot bishops. To be sure, he is far more zealous in seeing to it that pervert priests get the bum’s rush. But as far as bishops go, he is as reluctant as JPII to treat them like middle management who work for him. He appears to take the same, very eastern, view of the papacy that JPII articulated in Ut Unum Sint. If I’m right, then the best place to turn for an understanding of why these Popes act that way they do toward bishops who were idiots is… to ask Rod Dreher’s Orthodox bishop. He, along with the rest of the eastern Churches, will be happy to explain that the Pope is not the Supreme Maximum Leader who can run about treating brother bishops as mere underlings who work for him. If I’m right (and I’m pretty certain I am), the Pope feels himself very hindered by the Church’s teaching on collegiality. So, for that matter, do the Orthodox, who have their own troubles with pervy priests and the bishops who love them.

Well, for one thing, I don’t think the Pope should “expel a huge number of bishops from their sees.” How about just one or two of the worst ones?
For another: Bishop Jacques Gaillot, now of the titular see of Partenia, got sacked from the see of Evreux, France, by John Paul II for preaching heresy and generally acting like a public loonybird. So it can happen, and in Gaillot’s case, the Pope was absolutely right to do what he did. But look, is whatever nutball thing Bp Gaillot was preaching in Evreux worse than systematically facilitating the rape and molestation of Catholic children? Hmm.
For a third thing, does Shea realize that the Holy Synod of Bishops of the Orthodox Church in America last year sacked Bishop Nikolai of Alaska for, among other things, ordaining a registered sex offender? That the last Metropolitan (e.g., the primate) of the OCA resigned before he was set to be deposed by the Synod for his corruption, and is now living under severe liturgical restriction? That the Antiochian Orthodox Church in the US sacked one of its bishops after he got drunk and grabbed a woman’s breast in a restaurant? The Ochlophobist has a list of other cases of Orthodox synods deposing bishops; he also mentions the case from a few years ago of Archbishop Spyridon, the head of the Greek Orthodox Church in America, who resigned after facing mounting protests from priests and laity over his autocratic management style — which included firing people as part of an effort to protect a drunken monk who sexually assaulted a man. A popular uprising at Spyridon’s misrule forced him out.
None of these cases, in my view, involved facilitating the chronic sexual abuse of children by pervert priests. True, Cardinal Law of Boston resigned in the face of massive unrest over his misrule, so that’s a case like Abp. Spyridon’s. The point is, though, it is demonstrably untrue that the Orthodox don’t get rid of problem bishops. The mechanism includes the Holy Synod. What is the mechanism in the Catholic Church except through action of the Pope? If the Pope wants to do this, he can do this. Bishops are servants of the people of God, and if they prove by their conduct that they cannot serve the Church effectively as leaders of their dioceses, then the man responsible for putting them in place should do a Bishop Gaillot, and find somewhere else for them to serve.
Obviously the Orthodox would not look kindly on a Pope ruling autocratically and sacking bishops willy-nilly. But to my knowledge — and please, someone who knows Catholic canon law correct me if I’m wrong — no synod within the Catholic ecclesial structure can appoint or remove a bishop; that power rests solely with the pontiff. It’s a power that should be used rarely, in my view. But if the power exists, and it’s not exercised, no matter how badly a diocese has been misgoverned regarding the sexual exploitation of children, people are entitled to wonder why not. Saying “it just doesn’t work that way” is not a good explanation, nor is citing the supposed unwillingness of the Orthodox to sack their bad bishops, when there are several contemporary examples in the vastly smaller Orthodox churches in America. To say otherwise smacks of clericalism.