Similar to "keep on a short leash". Yanking someone's leash means to verbally admonish them, usually constantly and for things that don't warrant it. Often done until the person whose leash is being yanked stops acting or talking a certain way and loses a part of what made them themselves. This is often associated with a controlling relationship.
Derived from the concept of pulling on a dogs leash when he tries to go somewhere or do something that the owner doesn't approve of.
See also: Pussy whipped
Not to be confused with: Yanking your chain
Husband: *innocent joke*
Wife: Do you always have to do this? You are humiliating me, you're so insensitive, that joke was not okayandblablablablablablabla
Husband: I'm sorry, dear.
Husband's friend: Damn bro, she's really yanking your leash!