They also clapped after two other videos were played of Cottrell complaining about being labelled an extremist and media coverage of his case.
The disruptions prompted Chief Judge Peter Kidd to call for "quiet please" before warning Cottrell's supporters they risked facing contempt of court proceedings.
"I expect complete silence throughout the course of this case," he said.
If the behaviour continued, the judge warned: "firstly, you'll be removed from this court and, depending on what happens, I've got contempt powers".
Cottrell, Neil Erikson and Christopher Neil Shortis were convicted and fined in 2017 over the beheading video, involving a dummy made of pillows and red liquid squirting from its head.
One of the group wore an imitation of a Muslim head covering while one or more shouted "Allahu Akbar".
The video also showed the group chanting "Aussie, Aussie, Aussie" while carrying and driving around with flags.
Cottrell complained about being accused of neo-Nazism, "whatever that means", coverage of his court case, and also took aim at the government and media being "against the will of the working class".
He previously tried and failed to take his appeal to the High Court before also being knocked back by the Supreme Court.
Cottrell's lawyer John Bolton plans to argue the case on constitutional grounds after it resumes in the County Court on Tuesday.