Police found the first boy a short distance from the school and arrested him on a charge of wilful damage. More charges may be laid.
Officers then went on to the school bus to retrieve the tool allegedly used in the destruction, but the spokeswoman said the boy with the implement tried to hide it then refused to hand it over to the officers.
She said the boy then dropped the tool and his brother, aged 15, picked it up and threw it out of the window.
The spokeswoman said the boy was then told he would be arrested for obstruction and both brothers then allegedly attacked the two police officers, pushing and punching them before the officers ended up wrestling the pair on the ground.
She said during the melee officers used pepper spray on the two boys in an effort to subdue them after they allegedly refused to comply with police direction. Both were arrested on charges of obstruction and assaulting police.
Further charges may be forthcoming against the pair.
The spokeswoman said both officers suffered from residual pepper spray and one was given medial treatment and cleared to resume duties.
The three youths are expected to appear in the Kaitaia Youth Court next week.
The spokeswoman said it was disappointing that young children were involved in an altercation with police after allegedly refusing to comply with instructions from the officers.
In a statement, Mr Lowe said the school was working closely with police to assist them in their investigations but he was unable to comment on the incident as it is in their hands.
"What I can say is our school takes its responsibilities around the wellbeing of our students, staff and school community very seriously and we do not condone any violence in our school," Mr Lowe said.
"We have contacted our parents and other schools with students who may have observed the incident to offer any support that is needed. We have also contacted the Ministry of Education to ensure that we handle this matter well for all concerned."
