Will pet mice bite

Any animal can be mean, regardless of the species. It's a matter of disposition and intimidation.

An animal who is exposed to displeasurable situations from a source will dislike whatever it is that is causing it displeasure. Each time this happens, it results in a negative shift in its disposition toward the source (and what it relates to the source). The opposite of this being favorable situations, resulting in contentedness and a positive shift in its disposition toward the source. The way the animal reacts is determined by its level of intimidation, if it isn't intimidated by the unpleasant source, it will likely try to force it to stop.

Due a mouse's small stature though, one in good mental health is highly unlikely react aggressively toward people.

In short: if your mouse is being mean to you, it's probably mentally ill.