There are several potential causes for a rabbit to have blood coming from its mouth and nose, including:

Dental problems: Rabbits' teeth continuously grow throughout their lives, and if they become misaligned or overgrown, they can cause injury to the rabbit's mouth and nose.

Upper respiratory infections: These infections can cause inflammation and bleeding in the rabbit's respiratory tract, leading to blood coming from the nose and mouth.

Trauma: If a rabbit has been hit or struck in the head, it can cause bleeding from the nose and mouth.

Poisoning: Ingesting certain toxins can cause bleeding in the rabbit's respiratory tract.

Tumors: Certain types of tumors can cause bleeding in the rabbit's mouth and nose.

If you notice your rabbit exhibiting these symptoms, it is important to take them to a veterinarian as soon as possible for a proper diagnosis and treatment.