A player uses Bellows Breath, if I use Smoke and Mirrors in reaction to move a unit away from the location that was targeted with Bellows, how does this resolve?

Yes, you can use Smoke and Mirrors as a Reaction from Hidden to respond to Bellows Breath on the chain. Here's how it resolves:

When you reveal Smoke and Mirrors from Hidden (gaining Reaction per Rule 811/737), you swap two of your units at different locations — e.g., moving the targeted unit away from the battlefield Bellows Breath chose.

On resolution, Bellows Breath does not fizzle. The "same location" requirement is a targeting restriction for playing the spell, not for resolution (FAQ #7422, #9018). Instead, you choose one location among those where your originally targeted units are now present, and deal 1 damage only to the targeted units at that chosen location.

So if the moved unit ends up alone at your Base and the other targeted units remain at the battlefield, the Bellows Breath player can choose either location — damaging just the unit(s) there. Units not originally targeted (like the unit swapped in by Smoke and Mirrors) take no damage.