This is a question that I answered recently.
It could work but microdermabrasion is usually a more superficial procedure. Birth marks usually have a deeper component within the skin. Microdermabrasion is a superficial type of treatment that is not usually done to remove birthmarks, however. If done aggressively with more suction and more passes you can make the microdermabrasion reach deeper. There are some microdermabrasion machines that are medical profession strength that can be used more aggressively. Lasers, actual excision of themark, laser resurfacing, dermabrasion are other options.
Thanks for reading, Dr Young
Dr Young specializes in Facial Cosmetic and Reconstructive Surgery and is located in Bellevue near Seattle, Washington