I asked a German Warum? and he replied back Wie warum?! .
I do not know what it means when you put both Wie and Warum together. Google Translate says it means like why.
What would you have said in English instead of saying Wie warum in German?
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Well you were asking Why? and they answered basically What do you mean, Why?'
The phrase Wie Warum? implies that from their point of view the question does not make sense / is superfluous as it should be clear why (or Warum) something is or has happened.
Another case of Wie in a response (thanks for the reminder @Giorgio)
If you say, e.g. Mein Computer ist kaputt., someone might answer *Wie(,) kaputt?. This can either mean Was ist kaputt? (What's wrong/defective) or as well Was meinst du mit 'kaputt'? (similar to the case above).