Ahhh...it's complicated. I think "Du sao ____ cung" = Anyway.
I tried to talk it through with a Viet friend....but still don't get it!
Well in English "I don't need him either" is more natural, but that doesn't explain this one really...
I guess "dù sao...cũng" has to be used together. This is like "wúlùn...doū" in Chinese or "put-kuán...lóng" in Taiwanese. And the meanings of these phrases in these three languages are very similar: The two in Chinese and Taiwanese literally mean "no matter...". Probably the Vietnamese phrase "dù sao...cũng" can also be paraphrased so...
I guess in Vietnamese, you're standing by with your statement that you don't need him. It's probably a natural thing for the Vietnamese to say. Whereas in English, we already said "anyway". So we don't need to reaffirm that you still don't need him. Even though, we could also say "Anyway, I still don't need him". Just a guess.