I have a 6 month old male shih tzu, and just brought home a 3 month old female shih tzu. My male keeps on trying to mount the female. Can he hurt her by doing this?

Well yes, if he is heavy enough . I would redirect him. When you see him do this get his attention and ask that he sit, then reward him. He will eventually get the idea that his behavior is not wanted, not only by you, but also by the female. Most often mounting is a form of excitability, not always sexual, and it can be a means of playing. But it is still not something he needs to do. You must teach him not to. Also the other option is to remove the female from his reach. And do not allow physical interaction until he is sitting and then she is allowed in his territory. Its all about getting him to listen to you. And that your setting limits, this is one of them.