In 2018, the test will change from liquid-based cytology to human papillomavirus (HPV) screening.
Prof Cox was unhappy the committee endorsed the change last November. He had not agreed, and the committee was supposed to operate by consensus, he said.
New Zealand should consider a phased approach to the new test, he said.
"We've decided to go the whole hog and go to a completely different test and do it five-yearly, instead of three-yearly.
"Though that may prove to be not a bad way to go in the future, my initial look at it suggests that it's got rather large risks.
"I don't think the Ministry [of Health] have been as interested in differing views as they should have been." He had been a committee member for one year.
Prof Cox spoke at the annual Cartwright Forum in Auckland yesterday. The forum's theme this year was the cervical screening change.
The keynote speaker, Prof Marshall Austin, a pathology specialist from the University of Pittsburgh, travelled to New Zealand for the forum.
Prof Austin told the Otago Daily Times the new test used relatively unproven technology.
He said clinical trial data suggested it was less sensitive than the cytology-based system.
New Zealand should be cautious about changing a proven cervical screening programme, Prof Austin said.
"There are some countries that are thinking about going in this direction. None of them have actually started doing it yet.
"The irony in a way is that they are really proposing an experiment, and that has special meaning in New Zealand because everybody knows that there was another experiment in New Zealand," Prof Austin said, referring to the Cartwright Inquiry.
National Screening Advisory Committee chairman Prof Ross Lawrenson, in a statement, said the committee "collectively agreed" to endorse the HPV decision last November.
"The committee expects and promotes robust debate in reaching its decisions, but once decided, the committee expects its members to publicly support them." "Unfortunately, Associate Prof Brian Cox has been unable to abide by the terms of reference, despite the committee seeking an assurance from him in May.
"In light of that, the committee agreed unanimously to replace Prof Cox." National Screening Unit clinical director Jane O'Hallahan said HPV primary screening would save lives.
Other countries were moving to HPV primary screening, as it was safer and more sensitive at detecting cancer, Dr O'Hallahan said.
"When planning the move to primary HPV screening in New Zealand, the Ministry of Health commissioned research using New Zealand and international data.
"That research shows that primary HPV screening is more effective for women than the current cytology test," Dr O'Hallahan said in a statement.