Bleeding in the mouth is often caused by mouth sores, gum (periodontal) disease, or by a low platelet count (cells that help the blood clot). Low platelet tallies can be a reaction of chemo or radiation treatment. 

Ordinary activities, such as, brushing or flossing teeth can cause bleeding. Side effects of chemo or radiation can incorporate dry mouth or mouth bruises, which can bleed.

Here are some preventive tips mentioned

• Rinse your mouth gently with ice water every 2 hours.
• Suck on ice chips. (Avoid hard candies if your mouth is bleeding.)
• Rinse your mouth or your teeth with a soft toothbrush after eating. Rinse the toothbrush in hot water to soften the bristles even more.
• Use soft foam mouth swabs or gauze wrapped over a Popsicle stick or tongue depressor to clean teeth if a soft toothbrush causes bleeding. 
• Avoid store-bought mouthwash. See Dry Mouth to figure out to make a soft mouth rinse.
• Eat foods that are soft, smooth, and high in calories and protein. Refrigerated soft foods, such as ice cream, applesauce, puddings, and yogurt, can help because cold helps to slow the bleeding.
• Puree hard foods, such as apples, pears, etc., in the blender.
• Avoid hot drinks, such as coffee and tea. Heat enlarges blood vessels and can make bleeding worse.
• Put cream or salve on your lips to prevent dryness.
• If you wear dentures, keep them out of your mouth, especially if they don’t fit well.
• Avoid aspirin products. Check labels of over-the-counter drugs to be sure they don’t contain aspirin or check with your pharmacist.