A lack of funding to deal with violent children is also hurting children with disabilities, the Northland Principals' Federation says.
Federation president Pat Newman said he was close to advising schools to start suspending pupils who were a safety risk.
Other principals, who have supported his stand, said the funding squeeze was limiting the prospects of children facing physical and other challenges.
Kaeo Primary School principal Paul Barker said the saddest case he had to deal with was a boy who had a cleft palate repair and badly needed speech therapy.
The boy had been turned down by the Education Ministry at his previous school, Mr Barker said.
Some help was granted at Kaeo after several attempts, but it was not much.
"We were allocated a really fine speech-language therapist. But we were allocated two visits per term, for just two of the four terms. That was it," said the Kaeo principal.
"It's kind of developed into a system where the special teacher will come into the school; show the teacher-aide a few little things to do, and off she goes to her next person."
Mr Barker said he did not blame the specialist teachers, who were overworked.
Kate Lowe, the boy's mother, said when her son turned eight she was told by the ministry there would be no more funding because he had reached the age limit.
She said that despite requests from the school, and a recommendation from Middlemore Hospital experts, the Ministry refused to fund any more speech therapy.
She said she had done her best to help her son at home but, now aged eleven, he was still struggling to make himself understood.
"He is very aware that he's different and that he has speech problems and keeps asking me when he will be able to speak properly," she said. "Because he's now at an age when it's become embarrassing for him.
"So quite often when he's put in a position [socially] he will choose not to speak - which is not the best thing. So we're all pretty dispirited by it."
The ministry said it did not have a rule that children not get speech therapy and that should not have been give to the mother as a reason for declining support.
Spokesperson Katrina Casey said the ministry did prioritise speech therapy for children aged 5 to 8 because that was the age group most likely to benefit, and it had been decided Ms Lowe's son would make more progress if she were given strategies and exercises for him to practise at home.
"We've looked at [the boy's] overall situation to check if he's getting the learning support he is entitled to," she said.
"He has some high needs, and it looks like his support diminished after December 2014. We are now looking into why that is, and how we can re-establish it."
Mr Barker said Kaeo school had welcomed a number of refugees in recent times from Auckland, who needed extra help to cope with school.
Some were children sent up north to live with grandparents by parents who could not afford decent housing in the big city or who had succumbed to drug or money problems.
He said the Auckland children arrived stressed, distracted and well behind with their learning.
"There's been research that says children who move schools lose six to eight weeks [of] learning. Just last week we had a child join us who moved schools twelve times - she was in year four."
Mr Barker said he had all but given up trying to squeeze money out of the Ministry to help such children because the process was long, complex and mostly unrewarding in terms of the paltry sums eventually granted.
Kaeo School was spending about $120,000 a year from its dwindling operational budget to provide teacher aides and special programmes for them .
Principal Bruce Crawford from Hikurangi Primary School near Whangarei said one boy with cerebral palsy who loved school could only attend for three days a week because that was all the support the ministry would provide, and the school could not afford to top up the funding.
The boy, who uses a wheelchair, has a purpose-built toilet and shower at the school and needs help to use it, Mr Crawford said.
"The Ministry will make me out to be the baddie because I'm the one saying 'No, you're not providing him with enough teacher-aide coverage and I'm not prepared to have him in the school because of the extra demands it places on the class-room teacher'," Mr Crawford said.
Te Tai Tokerau principals said almost every school in the north had a similar tale to tell - and there was simply not enough funding available to help the growing numbers of violent children - and those with learning and physical disabilities.
Mr Crawford said he would put his foot down over teacher-aide funding.
Ms Casey said the issue was raised with the ministry by the principal last week.
"We suggested a reassessment of the child's entitlement to teacher aide support. We are happy to progress that further to see if we can find a workable solution so this child can be at school full time," she said.
Ms Casey said Northland schools were facing challenging issues with children with behavioural needs, and it had increased teacher-aide support by 20 percent because of that.
Funding for teacher aides providing in-class support had risen by 38 percent on last year, she said, and the Ministry had 91 specialist staff and Resource Teachers across the region working with schools and teachers.