I'm not an expert in laser systems but just from my layman's understanding:
A polished mirror surface might slow the heat build up a little bit but the best mirrors on the planet will still heat up if you're throwing enough energy at it; no mirror has a 0% absorption rate.
What's more, any imperfection on the surface will act as an focal point for the heat to build up; a spec of dust, a dew drop, a little oil from your fingertip, anything that can absorb the heat from the laser basically turns it into a hot spot that the laser will burn through rather quickly.
A polished mirror surface might slow the heat build up a little bit but the best mirrors on the planet will still heat up if you're throwing enough energy at it; no mirror has a 0% absorption rate.
What's more, any imperfection on the surface will act as an focal point for the heat to build up; a spec of dust, a dew drop, a little oil from your fingertip, anything that can absorb the heat from the laser basically turns it into a hot spot that the laser will burn through rather quickly.