Both 'our' Kirk and Mirror Spock knew the Mirror Halkans were toast. Once Mirror Kirk was back in charge, that was inevitable. But Mirror Spock also knew he had Mirror Kirk's ear, and that was all he needed to begin to make changes. Even something as pragmatic as getting Mirror Kirk to spare some Halkans, maybe a city or two worth, to work the mines was doable. Using local labor is always cheaper.
I though Mirror Kirk was pretty much sentenced to death already due to apparent waffling over his Halkan orders when Kirk was acting in his place.
I mean, he might very well have revolted, escaped, etc., but Mirror Spock couldn't count on achieving much with Mirror Kirk even if he did have his ear.
Or was the Empire flexible enough to say "All right, we're rescinding your execution this time! It's not worth the trouble!" as long as Mirror Kirk finally followed orders and killed the Halkans?