If you were to put a mirror into space and observe it moving away from you at half the speed of light, you would not see the past in slow motion. Instead, you would observe some interesting relativistic effects.
According to the theory of relativity, as an object moves closer to the speed of light, time dilation occurs. This means that time appears to pass more slowly for the moving object relative to a stationary observer. However, this effect is not noticeable at everyday speeds; it becomes significant as an object approaches a significant fraction of the speed of light.
In your scenario, the mirror would experience time dilation relative to you as the stationary observer. From your perspective, the mirror's clock would appear to tick more slowly than your own clock. This would mean that the time experienced by the mirror, including any reflections it may show, would appear to be slower compared to your own experience of time.
However, it's important to note that this effect would be reciprocal. From the mirror's perspective, it would observe your clock to be ticking more slowly while its own clock would appear to be ticking normally. This is due to the principle of relativity, which states that there is no privileged reference frame in the universe.
So, while there would be a time dilation effect, it would not create a direct observation of the past or a slow-motion effect. Both you and the mirror would perceive time differently, but the observed reflections in the mirror would not appear to be in slow motion.