Use WOULD YOU MIND...? as a polite way to check if something is, or represents, a problem to another person. "I WOULD MIND" means "It would bother me" or "It is a problem for me" or "It is uncomfortable for me if...".
Technically, if someone asks you, "WOULD YOU MIND...?", you should answer "Yes, I WOULD MIND" if it is NOT okay with you. i.e., "Don't do that!"
You should answer, "No, I WOULD NOT MIND" if it is fine with you...if it is no problem. i.e., "Sure! No problem!"