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can my doctor fire or dismiss me as a patient

Patient non-compliance (non-adherence). When the patient fails to follow the treatment recommendations established by the doctor. (Which is why it is so important that you and your doctor make treatment decisions together.)
The patient’s failure to keep appointments. Patients make appointments, then cancel them at the last minute, or don’t show up at all. From the provider’s perspective, that means a window of no income in addition to the fact that the patient isn’t getting the help he or she needs.

A patient’s rude or obnoxious behavior. No patient should ever be rude or obnoxious. It’s a form of abuse. Just as we patients should fire a doctor who behaves this way, it’s fair that a doctor should fire a patient for such poor behavior, too.
Non-payment of bills - money owed by the patient, but usually not the patient’s insurance.
If the doctor’s practice is closing. Just like the rest of us, doctors close their practices. They may sell them, or retire from practice, they may die, or just close their doors.

A relatively new reason for dismissal seems to be based on the type of insurance a patient has. In recent years, more and more patients report their doctors are firing them for no apparent reason (at least they are not told what the reason is).
The one thing these patients have in common is that their payers are those that reimburse providers at very low rates. As reimbursements have gone down, the number of patients reporting dismissals from their doctors has gone up. If you aren’t sure why your doctor has dismissed you, you may want to better understand why doctors don’t want to accept some insurances.