Yes, it’s reflecting the beam, but if I painted it in black…
Is all laser-power because of heat - what if I gryo-froze the object, could I cut it at all?
A CO2 laser will cut a mirror very nicely, because glass is a strong absorber at 10.2µ…
Mirrors that are designed to reflect laser beams need to be “first surface” - no glass in the way of the beam. If the laser is high enough power, the mirrors need to be able to handle the energy of the beam, or they will become damaged.
As for freezing - a cutting laser puts enormous energy into a very small area. There’s no way that simply cooling the object is going to overcome that amount of heating (the temperature at the focus point can be tens of thousands of degrees - a few hundred degrees below room temperature isn’t going to make much difference).
If you paint a mirror black, it is not a mirror any more.
Yes, any cutting a laser does is because of the heat it generates, so cooling the mirror will not help you cut it (though, going by what beowulff is saying, it won’t hurt much either).
There’s no such thing as a perfect mirror; even the best real world mirrors absorb some of the energy that hits them. So with enough energy you should be able to cut a mirror even with a light frequency it reflects.
Interestingly enough that’s not actually true, there are lasers that cut by other methods. Excimer lasers slice human tissue not by burning the tissue they strike, but by ablation.
In fact, this is one of the difficulties in working with high-powered lasers: You’ve got to make very low-absorbing optics to make your beam do whatever it is you want, lest they be damaged by it.
I see a red mirror and I want it painted black…
Just flip it over and cut from the back 
I have this Gary Larsonesqe vision of a guy intently cutting a mirror with a laser, while pieces fall off of everything else in the room, which is in flames.
I also picture some other guy just coming over with a glass cutter and cutting another mirror (or the same one the laser is working on perhaps?) in but a moment’s time.
The point here is that when you cut the paint, you see the reflecting mirror - so a thin layer of paint might not be enough…
This.
I was working with a high-power CO2 laser that we built, and was extremely frustrated because it had such a high internal energy density that the beam would seize upon any slight defect and get absorbed by it, thereby degrading it. Thenext shot would degrade it still further, and the subsequent shot would degrade it yet again, and on and on in a vicious cycle that lef me with a ruined mirror after several shots. fter which, of course, the laser didn’t work any more.
Extremely frustrating, because it was obvious this would happen. But I didn’t design the laser – I just had to make it work.
Often you don’t even need a defect – there are damage thresholds when the mirror itself fails. I’ve had that happen, too. as Der Trihs properly says, there’s no such thing as a perfect mirror. And if there was (like one of Larry Niven’s Stasis Fields), you’d find yourselgf running into paradox territory.
<claps>
Nitpick: I don’t think even Niven’s stasis fields were perfect mirrors. I’m pretty sure they have an absorption coefficient equal to their time dilation factor (which is really really close to zero, but not quite equal to it).
Now that’s some world class geekery there.
What happens when you lase water?
You’ve never had Laser Water?! Hot damn, tastes like cinnamon.
I’ve read discussions that claimed they were perfectly reflecting. Whence comes your variation?
You get a Water Vapor Laser:
It might just have been something I came up with, while trying to justify why they’d be (near)-perfect mirrors to begin with.
Not to hijack this thread too much, but (as I recall) Niven changed the way his Stasis fields worked over the years. In some of his stories, time completely stopped inside of a field, in others time simply progressed very, very slowly.