In addition to the issue Dave mentioned re: travelling at that way through the atmosphere, the next problem is what do you make your reflector out of, and how do you send someone up there to windex it?
Since it's not possible to make a perfect reflector, some of the beam's energy gets transferred to the 'mirror'. If you're using a beam with enough energy to cook a tank/missile/whatever then you need a reflector which is tough enough to take that heat.
But what happens when your mirror picks up some heat from the beam? It starts changing shape a teensy bit. So as the mirror warms up, it will reflect the beam slightly differently... and anyone who's fired a gun over long range can see how this is a problem when your range is from the earth into space and back again.
And the crack about windex? Yeah, there's dust in space. The more dust on your mirror, the more heat it absorbs... etc.
Don't forget the added complexity of firing a laser from the surface of the earth (which is rotating one way) to hit a satellite (probably rotating another way) in order to hit something which is also moving around...
Oh sure, there are ways to beat these problems. But people won't give you money to do that until you've proven it will work the 'simple' way.
(TBH mounting it on a herc isn't the simplest way of doing it either, but it's a hell of a lot cheaper and easier to 'sell' when you're done.)
