Reflective paint, ablative coatings, internal vacuum layer, heat insulation, thermally insensitive explosive and detonators, etc.
Even if those conditions are met, however, mirrors still make for surprisingly bad defense against weaponized lasers, simply because no mirror is 100% efficient. The 0.1-ish% of a well focused, high-powered weapons laser that doesn't get reflected by a ridiculously high quality mirror on initial contact will still damage and deform the mirror, thus allowing more and more of the laser's power to be deposited in the target with increasing dwell time.
Laser weapons avoid destroying their own optics by, first, using optics tuned exactly to the specific frequencies the weapon is designed to fire, and second, by using relatively large focusing mirrors / lenses which keep the power/area on the weapon optics below dangerous levels. Even so, real laser weapons have ridiculous cooling requirements to keep from destroying themselves with waste heat, which keeps their efficiency rather low.
There are other countermeasures that can be used against lasers, to be sure; mirrors just ain't one of them.
Are you saying that picking a coating with low absorption in the part of the spectrum that the laser is in doesn't matter?
I'm not sure I agree with you, since it makes other strategies (such as rolling the projectile in flight or using ablative materials) more effective if the projectile is slower to absorb energy from the laser.
The whole name of the game is to collect as little energy as possible, disperse it as evenly as possible (in non-important areas), and avoid deep penetration.
It doesn't magically stop the laser to paint it the right color, but choosing the right paint is an important part to penetrating laser based defenses.
If the attacker is just trying to heat up the bulk of the target until it melts, or is otherwise disabled, then a low-absorption coating would indeed slow them down. Such weapons have been proposed, but they're not especially effective anyway, and that's not how modern experimental military lasers are designed to work.
Weapons lasers are designed to focus as much power as possible into as small an area as possible in order to cause physical damage at the point of impact- blasting a hole in the thing, setting it on fire, etc. Heating the bulk of the target is a mere side-effect.
In that regime, anything less than 100% reflectivity is essentially pointless. Sure, it'll delay penetration, but not by any significant amount. Within a very tiny fraction of a second, the part of the laser energy that you do absorb in the target spot will be enough to destroy the reflective coating, and bring the full beam energy to bear. Unless your projectiles are expected to have flight times measured in milliseconds, the delay provided by a special low-absorption coating is utterly useless.
If you can prevent the enemy from dwelling on a particular spot, then things look much better. If you can screw up their targeting quickly enough, maybe you can actually prevent damage to the reflective coating after all. Even if you can't, maybe you can keep the laser occupied with constantly eating through fresh areas of reflective armor, never absorbing the beam's full power. But at that point, it's not the low-absorption coating that's saving you- it's your ability to screw up their targeting.
For example, the typical bullet rotates at ~200,000RPM. This is about 3,000 revolutions a second, or about 300 microseconds a revolution. Figuring a larger projectile could only rotate about a tenth of the rate, we get about 3 milliseconds per rotation on a shell.
At 3 seconds per revolution, I suspect that we're inside of the timing windows that talking about the efficiency of energy absorption and dissipation in the coating that the laser is striking is relevant, and we can begin to talk about the laser energy being dissipated over more than a single fixed point.
However, I suspect that such tactics (as high velocity spinning) can only mitigate the effects of the lasers and not stop them in isolation. It needs to be tied together with a coherent plan to dissipate the energy that areas do absorb and scatter the beam's focus using ablated coating.
In terms of energy absorption rates, energy dissipation rates, and ablative properties, picking the right coating for your mortars trying to pierce laser defenses is essential.
tl;dr: It's a synergy thing, since the low-absorption coating reduces the demands on screwing up their targeting, and screwing up their targeting reduces the demand on a protective coating.
Wait, I thought we were talking about the USA military? When have their weapons systems ever gotten cheaper? The only time they buy something cheap is when there is no more expensive option that does the same thing available (e.g. drones). If the only consideration is cost/shot, lasers will never be deployed. The point of TFA is that the new systems do things that haven't been done before, like stopping a mortar round in flight.