In this use the negative means answering in the negation. E.g Q: "Would you like some tea?" A: "I wouldn't mind!". You are answering 'yes', negatively, i.e. in

In this use the negative means answering in the negation. E.g Q: "Would you like some tea?" A: "I wouldn't mind!". You are answering 'yes', negatively, i.e. in the negation, by responding that you would _not_ mind to have some tea. It does not mean anything about the nature of the answer itself.