Moon cactus are actually two cactus grafted together. The red part can't support itself as it has no chloroplasts - those are what make plants green and is where photosynthesizing goes on. What you have left is the host plant, a type of Hylocereus. That baby coming up is attached to roots already so no need to re-root, just cut the dead part off. It looks rotten enough that it may come off by itself if you gently pull on it (the rotten part, not the green stem).
