Following an investigation, another pupil who filmed the incident, and then shared it, was also suspended. All three will go before the board of trustees disciplinary committee next week.
"We are absolutely appalled by this incident and will work through the school's disciplinary process to address it both punctually and appropriately," Paterson said.
"This type of behaviour goes against all that we value here at Waitaki Boys'.
"This is very much an isolated incident and the students responsible will be held accountable."
The video starts with four boys surrounding another young boy.
One of the boys and the victim trade punches, before the boy puts the victim in a headlock, knees him in the groin and pushes him into a fence and onto the ground.
He then holds the victim on the ground and punches him in the head.
Another boy, in a Waitaki Boys' uniform, then walks up and kicks the victim in the head.
The victim of the attack did not require hospital treatment, but Paterson said he could not go into further detail due to privacy reasons.
The school was working with police to support the victim and the incident had been referred to Youth Aid.
Sergeant Tony Woodbridge, of Oamaru, confirmed police were working closely with Waitaki Boys' on the incident.
The video was shared on social media yesterday and Woodbridge discouraged people from sharing and commenting on it.
"We would hope that people would keep their comments to themselves and look after things in their own backyard because it's no use pointing fingers, and appointing blame when you don't know the facts," Woodbridge said.
"These kids are young and have made some huge mistakes on the day that this happened, and it should never have happened."