Outrage over the Big Apple’s mental health crisis has reached critical mass — with lawmakers, first responders, patient advocates and everyday New Yorkers imploring the city to take meaningful action after a recent rash of violence.

Serious assaults by psychotic, untreated men — all in October — include a mentally ill street peddler who Friday put a cop in a coma by hitting him in the head with a metal chair at a Brooklyn nail salon.

Two days earlier, a deranged menace with a long history of violence against straphangers was caught on video shoving a woman head-first into an idling train.

“Have we lost our minds?” Gov. Andrew Cuomo asked Saturday, referring to the lack of laws to keep recidivist subway predators out of the system.

Even Mayor Bill de Blasio conceded Saturday that a probe into what’s going wrong is called for.

“We need to know more about that for sure,” the mayor said Saturday, when asked about the nail salon melee in Brownsville, which left untreated, bi-polar T-shirt vendor Kwesi Ashun shot dead and a veteran NYPD officer hospitalized in a medically-induced coma.

“Investigation underway,” the mayor said when asked about the city’s apparent failure in that case.

But more investigations — more city tax dollars spent on task forces, panels and reports— are not what the city needs, critics and reform experts agree.

What the city does need is to refocus the fortune spent on mental health — including the $1 billion over five years dedicated to the ThriveNYC “wellness” program — on New York’s seriously mentally ill, they say.

“De Blasio has been a disaster on all this stuff,” complained mental illness advocate D.J. Jaffe, an early critic of ThriveNYC.

The city has 239,000 seriously mentally ill residents, said Jaffe, the head of the city-based Mental Illness Policy Organization.

Of them, 40% — around 93,000 men, women and teens — are receiving no treatment, Jaffe said, despite being in the throes of serious psychosis, largely schizophrenia and bipolar disorder.

All of them cycle through three “choke points,” Jaffe said: hospitals, jails and homeless shelters.

And so the city knows these 93,000 untreated, seriously mentally ill New Yorkers by name, including the small, single-digit fraction who are at risk of committing violence.

That includes Rodriguez “Randy” Santos, a homeless psychotic blamed for the Oct. 5 bludgeoning deaths of four homeless men in Chinatown.

“Clueless,” Keisha Hogans of the nearby Mariners Temple Baptist Church described ThriveNYC officials’ response to her days after the attack, when she requested help hosting a mental health forum.

But ThriveNYC staffers did come to the neighborhood — to hand out brochures, she said.

The family of Ashun, 33, had struggled to keep him healthy, calling in a city Department of Health mental health crisis team to evaluate him, only to be told he was not a threat — and that they should call 911 if that changed, his sister said early Saturday.

“I said we have to wait until he’s physically violent to call 911? We’re reaching out for help now,” Bartley told The Post she said to officials.

“It’s ludicrous to have laws that require violence,” Jaffe said. “Laws should prevent violence.”

Instead, the city’s first responders are often the only line of defense against violent crises.

“What we’re seeing is more and more incidents of mentally ill really acting up and resisting any kind of apprehension or pushback, whether from the public or the police,” said Ed Mullins, president of the Sergeants Benevolent Association.

“As a police officer, I’m being put in a position that I may have to shoot him in order to stop that. It you look at all the police involved shootings, we’re seeing almost one a week,” Mullins said.

“This thing is very explosive, and the problem is that the public is silent on it, because it’s not their problem.”

“The mentally ill are not getting any help from the mayor or the city. We throw money, it doesn’t work,” he said.

“They need to come up with a better plan. We’re putting the public in danger,” he said. “We need a change. Cops want a change.”

Responders and the public are at risk thanks to “millions wasted on programs” that don’t help the seriously psychotic, agreed Mullins’ counterpart at the Police Benevolent Association, Pat Lynch.

And barely a day goes by when an ambulance worker isn’t assaulted — on Friday, an EMS worker’s nose was broken from a deranged patient’s punch in the Bronx.

“There definitely is an increase in assaults and violence on EMTs and paramedics,” said Vincent Vitale, president of the Uniformed EMS Officers Union.

A lack of money isn’t the problem, Jaffe said. It’s where that money is spent.

“Some 6 million is spent running and advertising the NYC Well phone number— if you’re feeling under pressure, call!” notes Jaffe.

“All of New York is under pressure! Why not spend that money on the seriously mentally ill?

“Take your outreach workers, and instead of having them talk about ‘wellness,’ put them at the exits of the jails, the hospitals, the homeless shelters, he recommends.

The city should spend money to support families, and for housing — he praises Fountain House in Manhattan— where the seriously ill can get treatment, he said — places where the mental health diversion courts can refer patients who commit only low level crimes.

“If we’re spending money, it should go to the people who need it most, not least,” he said. “Because the consequences are greatest for leaving them untreated, for them and for the communities.”

At the Goldmine nail salon on Saturday, the shattered front glass and lingering bloodstains on the floor were reminders of the previous day’s violence.

“Talking to themselves, screaming in the streets,” mail carrier Doris Watkins, 50, said as she walked nearby.

“Just the other day me and my daughter were walking, I had to push her to the side because the man walking toward us was talking all loud, yelling out obscenities, talking to himself. He looked disheveled and dirty.”

“I feel that the mayor needs to start focusing on the real stuff, he’s focusing on the wrong stuff. These issues are not going to correct themselves.”

Additional reporting by Sara Dorn, Khristina Narizhnaya, Georgett Roberts & Rachel Green