Is it polite to ask my mentor to recommend me to Professors she knows in the graduate school?
Yes it is polite and it is actually proper to ask a mentor for this in most cultures, I suspect. Some professors might be reluctant to do this, but I think not very many.
But what it actually gets you depends on the admissions system at the universities you apply to. In some, say in the US, it might have little effect on admissions but it places (and fields) in which professors hire their own students it would be much more valuable.
But in any case, having been introduced will be a small (at least) advantage if you wind up at one of these schools and it is a good idea to go meet the people you were introduced to. You might even be able to pick up a new mentor at the new place.