To mind something means it bothers you. If something matters, it is important.

It depends on the wider context. The phrase 'to mind' applies to a person's feelings or attitude. The phrase 'to matter' can apply to a person but also as a fact. For example, 'it doesn't matter to me' (I don't mind), but 'it doesn't matter if the wall falls down' (fact).

I can definitely see the confusion, since these would both translate to "(no) me importa" in Spanish. There is no difference in meaning between these two expressions, but there is a difference in structure. While you would say "I (don't) mind X", you must say that "X does(n't) matter to me". I hope that makes sense.

I don’t mind It doesn’t matter.

Chris is very correct, Adding to that some examples: I don't mind that at all. It doesn't matter. What matter is that to me (a noun in this case). Mind is when it's important to you, matter is when it's not important more in general.