I would like to ask, "Will this email address be removed from this mail group?"
The best I could come up with was, "这邮件地址会这个mail group除了吗？"
How should I ask this?
Better use active voice in Chinese, e.g. "這個郵件組會刪除這個電郵地址嗎?"
Indeed, I think the real challenge in your question is the two occurrence of "this". It is really awkward to have two "這個" in the same sentence. If you provide more information, I think we can make a better translation.
Edit @sazarando : for "Will this email address be removed from the Inside_Sales mail group?", I suggest "這個電郵地址會從'內部銷售'郵件組刪除(掉)嗎?"
(Instead of passive voice, I'd rather omit the subject.)