When copying a unit with Mirror image that has reduced might from switcheroo, does the copy have the reduced might as well?

No. The Reflection copies only the unit's printed traits (copyable traits — Rule 477.1.b.1.a), so it has the unit's printed Might, not the reduced Might from Switcheroo.

Switcheroo's swap creates a temporary arithmetic modulation on the original units for that turn (Rule 433.1.a). That effect isn't a copyable trait, and the new Reflection token isn't affected by it — same principle as Buffs and Gear not being copied (FAQ #10239, #9410). So if you Switcheroo a 6-Might unit down to 2 and Mirror Image it, the copy comes in at 6 Might, while the original stays at 2 until end of turn.