Mexican living in Japan wanting to go China. Is it possible to get a visa for more than 1 month?

It is hard to get it. Usually, the duration of stay for a single entry is 30 days at most. If you really have special reasons, you can try to apply for a longer stay, but it is assured that you can get it. You can consult more detail information from local tour agency or Chinese embassy or consulate.

If you cannot get a longer stay, you can enter China with the one you get and then extend it to stay a little bit long.