Not at all. In languages that are thoroughly immutable, it's copying, not immutability, that has a runtime cost. Rust has mechanisms for avoiding these costs (moves and mutable references).
Furthermore, since the compiler's knowledge of mutability is directly related to its knowledge of ownership, one could argue that immutability actually makes code faster by dint of providing greater aliasing information (e.g. `restrict` in C) to the optimizer (though the Rust compiler has yet to actually leverage this optimization).
It doesn't, it was just grouped with the other two. But immutiblity-by-default could lead to slowdown.