Well, it was mutual in the sense that a new religious body didn’t suddenly pop into existence, as in the case of Protestantism.
Because it was schism, what you have are apostolic churches cutting off communion from each other.
So there are two other ways of phrasing the question:
(1) Who’s fault was the mutual split?
(2) Who, if either, retains the true Church?
As for (1), the fault was chiefly pride… and differing cultures, legitimate theological differences, and slightly different (but deciding) ecclesiastical perspectives (role of Emperor, what does “Universal Church” mean, etc.) So the fault was on both sides.
As for (2), you have to decide what makes for full communion in Christ’s Church. The Orthodox posits that it’s not communion with anyone per se, but retaining the orthodox faith (as they understand it). The Catholic Church says, yes, there is a center of communion: Peter in Rome.
So in the Catholic point of view, Orthodox left communion with Peter – the chief Apostle and successor, the Bishop of Rome (Pope). In the Orthodox point of view, the Roman Catholic Church really left orthodoxy and not communion with any particular church, since there is no ONE primary church in Orthodoxy that makes full communion.
In actuality, though, the split was Rome vs. Constantinople, and those churches influenced by the Byzantine East.
I’m Catholic so naturally, I have my perspective.
But I would posit that the Orthodox’s position, or any other Eastern communion (Assyrian, Oriental Orthodox)'s position, is circular. Because what you have is “True Church” —> orthodox faith —> “True Church” —> orthodox faith. That is, the true church is evident by the true councils, which suggests the true church, and so on. But the Assyrian church could claim the same. Or the Oriental Orthodox. All accept different councils, each with its own “orthodoxy.”