οὐ is the negative of the indicative, μή is the negative of the other moods, including the infinitive and the participle.
Example: ὁ μὴ πιστεύων οὐ σώζεται, the not-believing one is not saved, or he who does not believe is not saved. Here μή negatives the participle πιστεύων, and οὐ negatives the indicative σώζεται.