Is it true that you can get mouth cancer if you keep biting off the skin in your mouth? I have a habit of doing that sometimes

Not likely. Oral cancer has many factors in its etiology or causes. This is not one that i know of. However when you habitually bite your cheek or lip what you can do is cause the tissue to react to the irritation. What normally happens is that the mucosa will become callous from the deposition of kerratin protein from the epithelium. This manifests as a thickening and whitish color change.
NO! Biuting skin has no known carcinogenic effect.