"Not at all" is the first response I can think of. If you want to be absolutely clear, then use "No, I don't mind".
You can technically say "yes, I do mind", but this is a little blunt and unfriendly for native speakers to hear. We're usually more diplomatic, so we use a phrase to introduce bad news, then give a reason. We don't usually reject the request directly unless we are quite angry.
You've probably come across the "buffer" phrases already: "I'm sorry, but...", "I'm afraid that...", "Unfortunately, ..." and so on.
Do you mind of I sit here?
I'm sorry, but my friend is sitting there. She's just stepped out for a second.
Do you mind if I smoke?
I'm afraid that I'm eating at the moment.
Do you mind paying for dinner?
Unfortunately, I was about to ask you the same thing!