Ceremonial Killings were a Puritan thing but if you study carefully the new Puritan's that moved to Massachusetts looking for religious freedom often did use capital punishment such as hangings and stone pressure (victim is tied to the ground and stone slabs mounted on their chest until they cease to breathe).
Women were not exempt from such deaths.
However, for smaller crimes such as gossiping, Puritans would actually sew the gossiping women's eyes and mouth shut so they could see no evil or speak no evil. Sadly i do not know the exact name of this ritual/punishment.