In England breaking a mirror means seven years bad luck! 新年快乐。恭喜发财！

Cannot would be one word. The sentences sound a little odd, but I understand what you are saying. I might say: A broken mirror can never be truly fixed. And: Can a broken mirror ever really be fixed? Personally, instead of fixed, I would probably use the word repaired. Or I might say, “Can a broken mirror be put back together?”