As Sally Draper on “Mad Men,” Kiernan Shipka has been slapped, mixed drinks, smoked cigarettes, driven a car and, in a recent episode, cut her own hair and then got caught masturbating at a sleepover.

Shipka started as Sally Draper when she was six years old, which means she has no recollection of life before she was an actress. It wasn't until she shot a teen movie that she learned how to open a ...