Mirror cutting

I would be interested, how many Watts it takes to burn through a mirror. 1kW lasers are known to manage it, however I've seen a couple of vids, where blue lasers do the job.

Depends on the mirror.

Not just the mirror reflective surface, but the mirror glass thickness, the ambient conditions, the mirror glass composition, the mirror glass temper, the laser wave length, the laser diameter, the duration to penetration, and probably several other variables I'm forgetting. I wouldn't expect anyone to pin down all of these variables, but at least make some attempt.