When someone is punished by being made to leave a particular place, it's called banishment. If your new puppy chews up another of your dad's shoes, it may mean banishment to the backyard.
In the old days, banishment was a common punishment for serious crimes — exiling someone from their town or village was shameful, leaving them estranged from their family and community. One particularly well-known banishment occurs in the Bible, when Adam and Eve are banished from the Garden of Eden. Today it's more common to use this word in a less serious way: "My banishment from the kitchen was inevitable after I broke three glasses in a row."