Mutability can always be faster given perfect optimization, in the same way as self-modifying assembly code can always be faster. However, actually doing that optimization on a byte-by-byte level is basically impossible. Techniques such as immutability makes reasoning about how to optimize general cases much simpler.
This often ends up with the trade off of higher ram usage and lower cpu usage, but a good enough general optimization can give lower ram usage too. Bad uses of immutability done for dogmatic reasons can often give you higher ram usage, higher cpu usage, and more complex code. As always, you do need to watch out for what you're using where and why.
If you think about the DOM as the projected state of an application, immutable data structures allow you to very simply define a functions that perform the transformation from application state to the GUI data structures (e.g. the DOM). If the state mutates this can cause cascading state changes that make this function much harder to reason about.