A sprawling homeless encampment near the Intrepid Museum in Manhattan has been vexing business owners and passersby for months — but the city is effectively running a valet trash service for its rough-sleeping residents rather than clearing the eyesore.

The steadily growing shantytowns — haphazardly strewn with all manner of bicycles, electronics and garbage — have taken over sizable portions of West 45th and 46th Streets along Twelfth Avenue in Hell’s Kitchen, between the museum parking lot and an Amazon warehouse.

“You see how it looks? How dirty it is? How can you eat food and the next corner is smelly, dirty, nasty, crusty, disgusting?” a food cart owner at the corner of Twelfth Avenue and West 46th Street told The Post, adding that the campsite has been chipping away at his business.

He said despite calling 911 and 311 “a million times,” the city has never dealt with the encampment itself, only sending Department of Sanitation workers out to clear the trash.

“They take the garbage only, but nobody can move anyone, even 911,” the cart owner said, noting he’s had to move further down the block just to keep afloat, which, paradoxically, places him further away from the deluge of tourists entering or exiting the museum.

Mayor Zohran Mamdani’s hands-off approach, however, is earning him rave reviews from the encampment’s occupants.

“Mamdani is awesome. He, like, did a whole paradigm shift on homelessness and care,” said Markus C., who lives in an encampment on West 40th Street but visits the 46th Street shantytown roughly twice a week.

He said he loves Mamdani, and how the administration treats the Big Apple homeless community, noting it’s the first time he feels like someone cared about his plight.

“Before, when the police were doing their sweeps, the cleanups and site checks, there was a lot of pressure,” Markus, who’s been on the streets for a year and a half, said of the tactics under former Mayor Eric Adams.

Since Mamdani got into office in January, “I noticed that it’s a lot more outreach workers instead of sending police officers. So now we have, on average, about three different organizations” to check in on them, he said.

But the city’s apparently lackadaisical response flies in the face of the official policy even under Mamdani, which state that homeless encampment sweeps are performed through a seven-day process, starting with placing a notice at each site, followed by daily check-ins to offer people shelter services before the locations are cleared.

Officials confirmed to The Post that complaints about the encampments near the Intrepid have repeatedly come in to both the NYPD and Department of Human Services, with calls on July 1, July 5, July 6 and July 8 this month alone.

A security guard working the Intrepid parking lot said the encampments haven’t created problems for his team specifically, but that they’ve been a persistent annoyance for the general public.

“You get a lot of joggers that have to jump over them,” he said.

One of the homeless-hurdling runners, Rashid Mak, 37, said he passes the encampment daily during his morning jog.

“They don’t give me an issue, but them being here is the issue,” he said. “It’s the stench, it’s the trash, garbage. Just loitering here, littering.”

He added: “Obviously, it just kind of fosters that environment where it’s more tolerable for that kind of behavior.”

Two workers sitting in the Intrepid parking lot on their lunch break Friday said the gates used to be open for those living in the encampment, but that they were closed a few months ago because of the constant littering and the large number of schools and families bringing children by on their way to the museum.

They said the city and the owners of the lot were sick and tired of having to pick everything up.

Liam James, who lives at the West 46th Street encampment, said the Mamdani administration was initially trying to clear everyone off the streets, but seems to have since shifted tactics to focus on sending sanitation crews to pick up trash and outreach workers for wellness checks.

“If they show up they call them emergency sweeps. And that means they always show up anytime they want and say ‘we’re throwing away everything,’” noting they limit encampment residents to three bags apiece.

“So as a human, I’m only entitled to three bags of things. Obviously it’s not trash [they’re throwing away], it’s somebody who has luggage. It’s wild. Why would you throw somebody’s life away?”

James, who didn’t know his exact age but said he was in his 40s and has been living on the streets for “too many years,” said the trash pickups usually happen on Tuesday and Thursdays, so residents always have their trash ready on those days.

“With Eric Adams when they talked about sweeps … they would literally come in, they’d arrest me and then throw everything away. That was the way it was before,” he said.

“And then the newer mayor has been more keen on well, during heightened weather, like, when it’s stormy, taking action — bringing it in, at least temporarily, or helping get whatever was necessary.”

He wanted it noted that the people living on the streets — whether in the Hell’s Kitchen encampments or elsewhere — “don’t want to have to be in this situation,” and are seeking for it to be a temporary solution for shelter, not a permanent housing setup.

James Bilis, 35, from Jersey City, has been living on the streets for five years. He also heaped praise on Mamdani for the uptick in outreach services and the lack of enforcement.

“The homeless outreach, it’s been a lot of that. They walk around, they bring food to people all the time now. They bring supplies, try to give us shelters, there’s a lot more than before,” he said.

He said there are a lot more cops and outreach workers now, but that they mostly leave him alone after checking on him.

“I think with Adams, we would have been moved around a lot more. actually, it was a lot more moving around. now, it’s like they don’t, they don’t bother you as much. They don’t mess with you.”

— Additional reporting by Carl Campanile, Craig McCarthy and Hannah Fierick