Does a med spa in Mississippi need a medical director?

Short answer
The cited rules do not settle this — they name no "medical director" and Mississippi issues no med-spa-specific license; they do require a physician's license to prescribe or direct drugs or appliances for pay, and a physician on the premises for laser use.

Mississippi puts its supervision lines in the medical board’s rules, and the one that reaches a med spa most directly is the laser rule. The statute defines the practice of medicine as suggesting, recommending, prescribing, or directing any drug, medicine, appliance, or other agency for the cure, relief, or palliation of any ailment for compensation, and requires a license from the State Board of Medical Licensure before practicing. The Board’s laser rule declares the use of laser, pulsed light, or similar devices for invasive or cosmetic procedures to be the practice of medicine, limited to physicians and those directly supervised by physicians, with a physician on the premises and directly involved in the treatment if required. Physician assistants practice with physician supervision, may perform any delegated medical service within their training that forms part of the physician’s scope, are the agents of their supervising physicians, and supervision means overseeing and accepting responsibility for the services rendered. The Board of Nursing lets a registered nurse assign the administration of patient medications to other licensed nurses only, except as its Part 2860 sets out. On the cosmetology side, esthetics is defined as massaging the face or neck, brow work, lash and brow tinting, waxing, and stimulating, cleaning, or beautifying the face, neck, arms, or legs by hand, apparatus, or cosmetic preparation, and excludes the diagnosis, treatment, or therapy of any dermatological condition; the cosmetology board’s rules forbid any service or tool that penetrates the skin below the epidermis, forbid practicing medicine or surgery and excising moles or skin tags, and allow dermaplaning only with a disposable, non-surgical 10R rounded edge butterblade. None of the sections cited here names microneedling or a medical director.