In this sentence, MIND is a verb, and has a meaning similar to CARE, OBJECT (the verb form), or HAVE A PROBLEM WITH. " and he might answer "No, I don't MIND" which means "No, I don't HAVE A PROBLEM WITH that", or "That's OK WITH ME". In your example, imagine some context: "I sat in front of her, blocking her view of the TV.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.