Saying ‘Yes, I do. / No, I don’t’ in English is more polite than just saying ‘Yes. / No.’ That’s why short answers are very commonly used.
To form the short answer, you use the first word from the question. (This is either an auxiliary verb or a form of ‘be’.)
Use the long form (he does) in affirmative answers (yes).
Use the short form (he doesn’t) in negative answers (no).