I mean overthrown by other party members, not by ordinary Chinese, of course.
I am not a specialist in Chinese politics, but the logic and Soviet analogy suggests that the party can directly depose only party officials like the General Secretary.
If one wants to fire a state official like the Chairman of the PRC (you called it President), then one has to make a vote in the legislature (in Chinese case, the National People's Congress), where the Communist party likely to have the majority or at least plurality (note though that in the Soviet Supreme Council since the 1970s the majority were non-party members).
And in Socialist type states the supreme legislature usually has huge powers, definitely enough to depose any state official including the Chairman, possibly even with simple majority.
No violation of constitution or court case against the Chairman is needed to depose him (like in the US), definitely.