Yes, you can be suspended or expelled for doing something violent to another student at the bus stop, or on somebody's front lawn or in a parking lot near the pizza place. The reason the school can step in like this is that those incidents of violence (or threatening, or bullying) have a huge impact on the culture of a school and the safety of the people who work and study in the school. It is all connected. A person who punches somebody at the bus stop may be someone who punches a student in the hallway. There may be a pattern of violence in that person's behaviour. A threat assessment may be done. Charges may be laid. The student may be required to attend an alternative program to get himself/herself together. The patch of grass one stands on while assaulting another person is the least important part of this picture.