Removing a mole near to the eye or along the edge of the eyelid requires expert care. Seek out a board certified, fellowship trained Oculofacial Plastic Surgeon -- an expert that can work precisely and safely near the eyeball. I have had patients travel from around the country to have me treat them for this kind of challenging removal - especially after they were turned away by dermatologists, general plastic surgeons, and family doctors. I have removed thousands of moles from around peoples eyes throughout my career. From the single photo you posted, in my office that would be removed under local anesthesia, and takes about 30 minutes. It is a painless procedure, and after-care would be some cool compresses for a few hours and a prescription for a special ointment that is safe for use around the eye. Full healing takes 6 months, but most of my patients with this sort of removal look great in about 3-4 weeks. I'd expect that could be removed with minimal scar. The key is to remove these without leaving a notch or scar at the edge of the eyelid and to not damage the eyelashes. Your mole is in a delicate, highly visible area on your face, so make sure you are comfortable that the surgeon you choose has extensive experience with these sorts of mole removals.
