Sure, they all support mutation. So do languages that are clearly not object oriented, like, say, ALGOL-60. (You can do mutation in Haskell, too.) So "mutation" is at least somewhat orthogonal to "object oriented".

What is object oriented? It's worse than "you can find an OO language that doesn't support feature X". There are (at least) two schools of OO, and they define OO differently. There's the Alan Kay school, where objects are independent entities that send messages to each other. And then there's the C++/Java school, where objects are less independent, and they call each other's functions.

What both of those have in common, though, is the idea of an "object", which is a bundle of a data structure plus code. In general, the associated code is the only code that can modify the data in the structure. (Yeah, I know, public data. But if you do that as your normal approach, then you're not really doing OO, you just have a bunch of structs that anyone can modify.)

An OO language, then, is a language that either supports or requires OO programming. Java, for example, requires it - a function has to be a member of some class. (Yeah, I know, it could be static, and it could not operate on any of the data of the class. Java still forces you toward OO more than C++ does.)

What about something like C? It lets you create structs, but it does nothing to let you restrict access to "associated" code, nor does it give you a way to associate code with the structure. (Yeah, I know, file static.)

I keep saying "yeah, I know" as I admit the exceptions to what I'm saying. None of this has rigid, clear boundaries. Still, there is a set of things that are generally OO, and a set of languages that generally encourage and/or support programming that way.