Moles on the face can be removed by a dermatologic surgeon
When a shave removal is performed, there is a 10% chance of the mole regrowing (raising up again). It can be shaved another time, or an excision could be performed. However, that leaves a line shaped scar which is more apparent than a shave removal scar. Most people opt for the shave. Make sure that pathology is checked to determine what the growth is. Rarely skin cancers can mimic moles on the face.
May be something called a fibrous papule and not a mole
or maybe a scar...tough to say without seeing what you're referring to but have a discussion with your doctor about the risks/benefits of having the area excised and sutured...chances are very slim if it's a mole of having it grow back afterward...or consider leaving it alone if it's not causing problems...
I would recommend a full thickness excision which is still a minor procedure and will actually heal better than a shave if done properly.