"They have to wait there for hours. It takes police off the road, it slows the system down. What it means is that almost around the clock our members are responding to mental health crisis, it shows the system is broken."

The state's misconduct watchdog has launched a criminal investigation into the violent arrest of a man in Epping after footage surfaced of him being rammed by a police car before an officer stomped on his head.

The man, who has bipolar disorder, had been waiting for mental health treatment at the Northern Hospital for 19 hours.

Then on Tuesday, a 24-year-old man walking around a car park with a knife became the latest person with suspected mental health concerns to be injured during a hostile interaction with police, after being shot by two officers outside a medical centre in Lilydale.

Police on Tuesday revealed they had been unable to roll out new mental health training for frontline members due to an "extraordinary" year of bushfires and the coronavirus pandemic.

When asked about what training police officers were being given around their interactions with the mentally ill, Mr Paterson said police had intended to roll out new specialist mental health training for all staff earlier this year before the bushfire season saw it put on hold.

Now, he said, the coronavirus pandemic meant police were unable to train in groups.

"This mental health training is a priority," he said. "When it's safe to go back into face-to-face scenario training we will absolutely be rolling out this training."

The incidents have renewed calls for health professionals to be involved in responding to critical incidents involving mental illness, rather than just police.

Police Accountability Project principal solicitor Gregor Husper on Tuesday said it was “so frustrating to hear" police repeat their commitment to mental health training.

“If I had a scrapbook for every time police try to explain away bad behaviour with training, it’s a smokescreen and they know it.”

“There have been numerous coronial inquests into fatal shootings of people with mental illness. These lessons have been discussed and explored many times before,” he said.

“Police constantly turn to training or new modules they have brought out, but the facts are there have been no significant improvements. No amount of training will change this. It’s a systemic, cultural problem."

Tim Marsh, chief counsel at Victorian Legal Aid, said on Tuesday that the prevalence of emergency service workers being first responders at health emergencies was of "great concern".

He predicted the state's mental health royal commission would make findings to address the matter, and said more mental health specialists were required to respond to acute incidents.

"When patients are admitted to psych wards, the two most common acronyms are BIBA (brought in by ambulance) and BIBP (brought in by police)," he said, adding he was not casting judgment on the actions of police in any specific incident.

"It’s a really difficult situation for everybody involved."

The incidents at Epping and Lilydale are the latest in a rising number of violent interactions between police and the state's mentally ill.

In May, a 53-year-old Narre Warren father was gunned down on the Monash Freeway at Dandenong North after lunging at officers with a knife.

In July, Gabriel Messo was shot dead by police after attacking his mother in a Gladstone Park reserve.

Both men had a history of mental health concerns.

With Paul Sakkal

If you or anyone you know needs support, you can contact Lifeline 131 114, or beyondblue1300 224 636.