Depending on the context, the phrase 'never mind' could be expressed in Hindi like : चिंता मत करो, कोई बात नहीं, परवाह न करो, कोई चिंता नहीं, कोई परेशानी नहीं, etc. and similarly, the phrase 'don't mention' could be expressed in Hindi like: कहने की क्या ज़रूरत है, शरमिंदा न कीजिए, ऐसा क्यों कहते हैं, बस रहने दीजिए, बस ठीक है, etc.

However, कोई बात नहीं and बस ठीक है appear to be more appropriate as these could generally fit in most of the contexts.

English term (edited): never mind. don\'t mention it.

never mind means do not think or get worried.

For "never mind" "कोई बात नहीं" is the appropriate translation. But for "Don't mention it", "Never Mention", etc., "कोई बात नहीं" isn't a good equivalent.
"Bool Jaav baat Ko" or "Zikir Karna Baand" or "Zikir Na Karo" or "Punah Prasaang na Uthav", etc., is a better option.