Teresa Man was walking from her apartment near Fourth and Brannan streets to an 8 a.m. coffee meeting in the Financial District on the morning of Friday, Sept. 13. Like on every workday, she strolled up Third Street past the San Francisco Museum of Modern Art. But this particular commute turned frightening.

She first saw the disheveled man wearing mismatched shoes — a black Adidas sneaker on his left foot and a black sandal on his right foot — pressing his face into the glass of the museum gift shop.

He, too, noticed her attire: a black sundress with white flowers in preparation for the stifling heat that would reach 94 degrees that afternoon. He asked Man what kind of flowers were on her dress and whether she had smelled them. She thought his questions were weird, and she rushed along.

Then, Man said, he told her, “I just want to smell your flowers,” grabbed her, pressed his nose and mouth into her breasts and attempted to remove her dress and bra.

“I screamed and said, ‘Get the f— off me!’” recounted the 28-year-old designer at a startup. She ran north on Third Street, and the man followed her. She told him she’d call the police if he didn’t leave her alone. He laughed and said, “The cops aren’t going to do nothing,” she recalled.

It’s one more terrifying encounter — seemingly fueled by drugs or untreated mental illness — in a city struggling to respond to these twin crises in any comprehensive, coherent way.

There are too few mental health beds. Too few drug treatment beds. A clogged psychiatric emergency room at San Francisco General Hospital that quickly releases people back to the streets. A criminal justice system that seems more intent on shifting blame than ensuring the public is safe. A mayor and board adding some new beds here and creating a task force there, but not making big change.

In March, Mayor London Breed appointed Dr. Anton Nigusse Bland to a newly created, $319,000 position of director of mental health reform charged with untangling this mess. So far, he’s announced there are a mind-boggling 4,000 homeless people in the city suffering from mental illness and addiction. But there’s no plan yet to address it, something Bland said would be a “multiphase, multiyear effort.”

It’s a stew of street misery and bureaucratic ineffectiveness just waiting to boil over — and too often, it does.

The attack of a woman in the doorway of the Watermark condominium building allegedly by a homeless man who said he was trying to save her from robots has sparked outrage, largely because the crime was captured on video. But it wasn’t an isolated incident — not by any stretch.

“We’re hearing it more and more,” said Supervisor Matt Haney, whose district includes the Watermark and the modern art museum. “When people walk outside, they’ve been accosted, assaulted, yelled at. A lot of that falls on my constituents — they’re angry and frustrated about it, and I’m angry and frustrated too.”

Gilles DeSaulniers, owner of Harvest Urban Market in the South of Market, reported being bitten this month by a violent homeless man he was trying to subdue. He told various TV outlets the man said, “Why are you even calling the police? They're not going to do anything.”

Last month, Jean-Marc Gorce, owner of XOX Truffles in North Beach, reported being put in a choke hold by a man he had ordered to leave the shop for disturbing other customers.

Christine Tamajong, 56, said another terrifying incident happened to her. She said she was walking on South Van Ness Avenue near 14th Street in April when a stranger punched her in the back of the head. She called 911, and an officer responded.

“The officer told me, ‘You can press charges, but the judge will probably drop it. It’s not going to go anywhere,’” she said, adding she opted not to press charges. “Too much hassle, too much paperwork, too much headache. ... It’s a beautiful city, but there’s something broken somewhere.”

That’s for sure. Supervisor Rafael Mandelman said he’s heard dozens of stories like these — including multiple incidents of people getting punched in the face by strangers — since taking office in June 2018.

“Being around people who are high and out of it does not make you feel safe,” he said. “And right now, if you’re in San Francisco in a public space, you’re around a lot of people who are high and out of it.”

He’s the chair of the board’s Public Safety Committee and co-chair of the city’s meth task force. A lot of the psychotic behavior on our sidewalks stems from meth, which often causes users to act in a scary, belligerent way, he said. S.F. General’s psychiatric emergency room is overwhelmed with meth addicts, and, in Mandelman’s words, the hospital holds them “only so long as you’re a maniac.” Once they’re sober, they’re released — often to go find more meth.

Mandelman said the task force has “again and again” discussed the idea of a meth sobering center where police could take people they believe are on the drug to rest and sober up. He believes the city needs two or three of these and said he’d gladly accept one in his district. It would remove meth addicts from the streets without clogging hospital beds.

The idea makes a lot of sense, so of course it has gone nowhere. Why not?

“Because everything takes forever,” Mandelman said, visibly frustrated by the inaction that plagues City Hall. Welcome to the club, supervisor.

Overall, violent crime in San Francisco is down, falling 14% from July 2018 to July 2019. Reports of aggravated assault dropped 11% in that time span. But anecdotally, stories of out-of-the-blue, psychotic behavior toward strangers seem to be increasing.

Officer Robert Rueca, a spokesman for the Police Department, said the department doesn’t track whether suspects in reported assaults were under the influence of drugs or whether a psychological or medical condition contributed to the attack.

He did confirm that a police report of a sexual battery was filed shortly after 8 a.m. near Third and Mission streets on Sept. 13.

“We are not identifying the victim at this time,” Rueca wrote in an email. “This incident is an open investigation. Due to the sensitive nature of the incident, we are unable to release any information.”

Teresa Man, however, wanted to share what happened to her. She said once she reached Market Street, the attacker finally headed in a different direction. She rushed to the coffee shop where her meeting was scheduled and phoned Chris Wong, a college friend in Toronto. Wong said they text constantly but rarely call each other.

“I thought it was either a pocket dial or possibly an emergency so I picked it up,” he recalled. “She was crying. I had a hard time understanding what was going on until she said, ‘I think I was just sexually assaulted.’”

She recounted what happened, and Wong told her to call 911. She did and said police took more than 15 minutes to respond. Police took a report and told her they would ask the museum for security camera footage.

Jill Lynch, a spokeswoman for the museum, said the museum’s security team has been in contact with the Police Department about the incident.

Man said she didn’t get the impression the officers who responded were going to try to track down the assailant because they didn’t rush off in pursuit. And she’s not optimistic anything will come of their investigation.

She moved to San Francisco just five months ago and said it feels much less safe than New York City, where she lived before moving, or Toronto, where she lived before that.

“It’s been a culture shock for me,” she said, adding that other cities have homeless populations, but the unpredictable, deranged people on the street give San Francisco a much more dangerous edge.

She was already uneasy about the city’s glaring wealth next to its extreme poverty and had started volunteering with ShelterTech, a nonprofit that brings technology to homeless people, including installing Wi-Fi in shelters.

But the sexual battery understandably soured her even more on her new city. People she told afterward advised her to carry pepper spray or even a Taser.

“If I have to get to that level of self-protection, I would leave. This is not the city to be in,” she said.

But one of the most disheartening elements of the crime was that Third Street was bustling with pedestrians on a sunny weekday morning, and not one offered to help Man or asked if she was OK. It seems in San Francisco these days, a woman being assaulted by a deranged man isn’t even worth a second glance.

San Francisco Chronicle columnist Heather Knight appears Sundays and Tuesdays. Email: hknight@sfchronicle.com Twitter: @hknightsf Instagram: @heatherknightsf