Mirror moving near the speed of light

The image will appear to move at the speed of light. If you move the mirror faster, the image will appear to exceed the speed of light.

Special relativity only forbids physical objects from going faster than the speed of light. There is no contradiction if non-physical objects such as images, laser beams, or shadows travel faster than light.

In the rest frame of the mirror, by symmetry your mirror image's velocity is the negative of yours. So in your rest frame, the mirror image moves at $frac{1/2+1/2}{1+(1/2)^2}c=4c/5$.

That's the speed that would be measured by a radar speed gun, for example (although only if the radar signal is not detected by the gun when it's reflecting off the "mirror image" (which is actually you), since otherwise you're measuring the speed of the mirror instead).