What kind of doctor can remove this sebaceous cyst on face without leaving a big scar?

Several types of cysts can be found on the head and neck, with one of the most common being an epidermal inclusion cyst. Given the nature of the cyst being related to the skin, an external incision is most common. Cysts can enlarge, so one way to mitigate the size of the scar is to address the cyst early. Several different providers are capable of cyst removal. You can consider discussion with a primary care provider to review your options.

It would be helpful to examine you to determine what the mass is that you see on your face.  If it is something that can be excised, I would recommend seeing a facial plastic surgeon or plastic surgeon.  

Dear nkace119,
it is hard to tell for sure, but if you do have a cyst there it can be removed surgically and with meticulous technique scars can be reduced. If you are considering a surgery, I would suggest you to consult a board-certified plastic surgeon. Only after a thorough examination you will get more information and recommendations.
Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery

I would recommend a Plastic Surgeon or Dermatologist. Small incision 2-3mm should be possible and the cyst can sometime just squeeze out. Recurrence is an issue but relatively uncommon. The wound may not even need sutures.