If I use Stupefy on an opponent's unit that has 2 might while I control an empowered Mel, Newly Awakened, does the opponent's unit get reduced to 1 might or 0 might?

The unit ends at 1 Might, not 0.

Empowered Mel's ability modifies spells you control that "give −[S]" — so Stupefy's −1 becomes −2 Might. But the "to a minimum of 1 might" clause is part of Stupefy's own effect, so the floor still applies: 2 Might − 2 clamps to 1. This is the same snapshotting principle as Rule 477.3.b — the limitation is applied when the reduction is generated, capping it at −1 for the turn. (If Mel weren't empowered, Stupefy alone would also leave it at 1.)