Is it safe to cut a dog's tail off?

No, that would be excruciatingly painful to the dog, and would have severe risk of complications such as uncontrolled bleeding and infection. You should have your dog evaluated by a veterinarian - it is possible the broken part can be bandaged or splinted until it heals, or the veterinarian may need to perform a surgical amputation of the tail (under general anesthesia and sterile surgical field to reduce the risk of complications).