I would like to postpone my first periodontal surgery (with new dds) visit a second time due to business scheduling. Will I be cancelled as a patient?

Office Policy. Your best bet is to ask the office at which you have an appointment. No one on this panel can possibly know how that office handles these situations. A cancellation fee may be requested, and if you like the specialist and the office, i would consider paying it.
Depends. Most clinics will accommodate you provided you give them a long notice. Ask your clinic what their cancellation policy is.
Unlikely as long as. It is unlikely that you will be cancelled as a patient as long as you give them sufficient notice and explain with a reasonable explanation as to why you need to cancel your appointment. Each office has a different policy in this regard. I suggest you call and discuss it with them.