golf ball size polyp on my cervix... how will they remove this and will they put me under?

No way to know. Why don't you ask the doctor who saw it and scheduled the surgery?
The cervix has no nerves to speak of (handy for stretching when giving birth) and small polyps are routinely removed at outpatient surgery, with no anesthetic at all. But yours could be different, and it would be imprudent to tell you what your case will be.