What kind of doctor treats and specializes in tongue cancer?

Several. Several physicians are involved in the care of patients with tongue cancer. An ear, nose, and throat physician (otolaryngologist); radiation oncologist; and medical oncologist may all be involved at some point during diagnosis and treatment.
Oral Surgeon, ENT. The first contacts should be with either an oral surgeon or ENT md. You might also have a need for an oncologist, as part of the treatment team. I would see the oral surgeon first.

Related Questions

Which type of doctor treats tongue cancer?

Depends. Exact location of cancer oral vs. Base of tongue matters. Ent, sometimes oral surgeon, radiation oncologist, medical oncologist, speech therapist, etc all play a role. We view a multidisciplinary discussion upfront as the optimal way to determine the best recommendations for care for all of our cancer patients. Consider centers with such an approach.
Oral Surgeon. This is usually treated by an oral surgeon and other doctors if any post surgical treatments are needed.

What kind of doctor sees somebody for tongue cancer?

ENT, and others. Many types of doctors may need to be involved. An otolaryngologist, radiation therapist and a medical oncologist may all be needed depending in the stage of the tongue cancer.
Ent. An ear nose and throat surgeon with interest and expertise in cancer.

Can you have tongue cancer, and if so, is it common for doctors to remove the tongue?

Yes. A person certainly can have tongue cancer. The type of cancer it is and the extent of the cancer will determine the extent of the surgery required.
Yes and no. Yes you can have tongue cancer. In fact it is one of the more common oral cancers. It is rare to have remove the whole tongue, but sometimes it is necessary.