Can smokeless tobacco cause oral cancer? If so, how?

Yes. Smokeless tobacco (chew, snuff, etc.) cause cancer by exposing the lining of the mouth or nose to toxins in the tobacco that can lead to cancer. They also can cause chronic inflammation that promotes the growth of cancer cells.
Smokeless tobacco . Over time the nicotine in the tobacco leaches out of the smokeless tobacco and decreases blood flow to the cheek and gum mucous membranes. This mucosa becomes more permeable to the 200+ cancer producing chemicals in tobacco. If you drink alcohol, the alcohol increases carcinogensis by extracting the carcinogens and enhancing their penetration into the mucosa. Stop if you can, or get help to stop.
Yes. By irritating the tisue, the tissue will change and become dysplatic (bad) and become theprecursor to cancer. Have your tissues checked by a dentist especially if they are whitish and have a washboard appearance.