" seems the better of the two. But, the sentence is awkward. Something using "Are you finished with " seems more natural to me.
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zhfanWhich question would be more correct?I would use the -ing form directly after through and a noun after through with. In any case I find the expression extremely limited in usefulness, so I hardly ever use it.
"Are you through your process (of doing smth.) yet?"
"Are you through with your process (of doing smth.) yet?"