It is called docking, cropping is done to the ears. Tail docking occurs in one of two ways. The first involves constricting the blood supply to the tail with a rubber ligature for a few days until the tail falls off. The second involves the severance of the tail with surgical scissors or a scalpel. The tail is amputated at the dock. Tail docking is done in modern times either for prophylactic, therapeutic, or cosmetic purposes. For dogs that worked in the field, such as some hunting dogs and herding dogs, tails could collect burrs and foxtails, causing pain and infection and, due to the tail's wagging, may be subject to abrasion or other injury while moving through dense brush or thickets.
In this day and age, it is usually done for cosmetic reasons and for nothing else. That is not a good enough reason to maim your beloved pet.
This is surgery and you must take it to the vet. When you do, you will sign a release form which states you will not sue the vet should your animal die during the surgery - which can happen during any surgery. Is this really something you would risk to make your animal "look" a certain way?