I know that trophies and stars on 150cc also count for the lower grand prix cups as well (i.e., they stack). Does 200cc and mirror mode work the same way? If I get three stars on a mirror mode cup, does it count as three stars for the same 150cc cup? What about for 200cc down to 150cc or mirror?
According to Gamefaqs, Mirror mode is independent from each other category.
But 200cc should stack with the lower 50cc, 100cc and 150cc cups, as it's just an upgrade of the same tracks.
Anyway you can try it by yourself. (I don't own the game, so I can't verify this.)