Will I be able to visit other countries with a student visa during my stay in China?

Margot, do you hold the X1 type or the X2 type? If it's the X1 type, I suppose you must have obtained a temporary residence permit. The permit, functioning as a multiple entry permit, will allow you to leave and enter freely. If you are holding the X2 type, it should be specified on the paper itself whether it is a double entry type or single entry type.