It depends on context, i.e. the phrase you are replying to, but it is usually along the lines “(but) yes, I can!”, “(but) yes, I do!”, “(But) yes, it is!”… like this:
You can’t do that! - Doch! → Yes, I can!
You don’t believe that BS! - Doch! → Yes, I do!
That can’t be true! - Doch! → Yes, it is!
and so on… It is the very spirit of contradiction. That sketch translates full of doch! into German.
Now translate “Nicht doch!” and explain in which context it can be said 
BTW, French translates doch simply as si, or mais si (which is not the same as oui or mais oui, and is not Spanish either, although it looks like it was). But nicht doch! does not translate as non si nor pas si, as far as I know.