Yes, boxing is a safe sport, because the injury rates are not higher for boxing than they are for other sports. Boxing is too often associated with mixed martial arts and caged fighting, when really boxing is a fine-tuned sport with rules about safety and proper decorum. When done right it is safe.
Boxing is a very dangerous sport, responsible for people getting an unusual amount of concussions. There is also a condition boxers are prone to getting, called dementia pugilistica. It's actually quite common in boxers, and is a devastating disease that causes dementia. Full-contact sports may be thrilling for some to watch, but they do put incredible stress on the body, and people who participate in these sports may pay for it in the long run.