According to our current understanding of physics, it is not possible for any object with mass, including ourselves and any spacecraft, to travel at or beyond the speed of light (c) in a vacuum. As stated in Einstein's theory of special relativity, the speed of light is an absolute speed limit in the universe, and as an object with mass approaches the speed of light, its mass would increase infinitely, requiring an infinite amount of energy to reach or exceed the speed of light. This is practically unattainable.
However, let's entertain the hypothetical scenario you presented: placing a mirror in space and looking into it while traveling at twice the speed of light (which, again, is not physically possible). In this imaginary scenario, we would need to examine the consequences based on the principles of special relativity.
According to special relativity, as you approach the speed of light, time dilation and length contraction would occur. Time dilation means that time appears to pass more slowly for the moving observer (the person in the spacecraft) relative to a stationary observer (someone on Earth, for example). Length contraction means that the length of the objects in the direction of motion appears to shrink as measured by the stationary observer.
If you were somehow moving at such an impossible speed, the view in the mirror would likely be severely distorted due to the combination of time dilation and length contraction. Here's what might happen:
Time Dilation: As you approach the speed of light, time would pass much more slowly for you relative to the stationary observer. Your perception of time would be significantly different from that of someone on Earth. Consequently, if you looked into the mirror, you might see a slow-motion version of yourself and your surroundings.
Length Contraction: The mirror itself would appear to be shortened along the direction of motion from the perspective of the stationary observer. Therefore, the mirror might look elongated or squished to you in the spacecraft.
Visual Effects: Since light itself travels at the speed of light, the light rays coming from your reflection on the mirror would be subject to these relativistic effects as well. The way you perceive yourself in the mirror would likely be distorted and stretched due to the combination of time dilation and length contraction.
Again, it's important to stress that this hypothetical scenario violates the laws of physics as we currently understand them. No object with mass can travel at or beyond the speed of light, and any attempt to do so would result in paradoxes and contradictions within the framework of relativity.