If you are saying that it is not a slap but the rotational movement of the mirror that is responsible for camera shake, then it would be due to the law of conservation of the angular momentum, which would require camera to rotate in the direction opposite to the mirror.
The effect of the slap would be subject to the third law of Newton, just as in case of the opposing forces during dampening of camera movement.
One method to improve stability would be to make the camera extremely heavier than the (fast moving) mirror.
In this case the angle of camera rotation (and any other further displacement) would be decreased.
At some point the energy of all of these movements is transferred into heat.
Therefore, another option I see is to dissipate the energy of camera disturbance very quickly, much faster than the duration of exposure.
I am curious, whether material used by NASA is targeting this effect.
This would likely also help dampening due to the vertical movement of the shutter.