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To do this in Apple Mail:
If you're not showing the size of the emails yet, you should turn that on by going to View -> Columns -> Size
Once you're viewing your emails you list this view by largest emails first you can then save the large attachments and then delete the large emails you don't need first. This strategy will give you the most bang for the buck in freeing up the most space in your email for the least amount of work.
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