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.

Kiernan Shipka, aka Sally Draper, has some thoughts about the direction her character might take in the new season of Mad Men. She’d like to see the troubled kid act up. At an Emmys party, Shipka ...