The city is approaching a terrible milestone — nearly 10,000 people have suffered cancers linked to the toxic dust and smoke at Ground Zero, The Post has learned.

With the 17th anniversary of the Sept. 11, 2001 terror attacks a month away, the federal World Trade Center Health Program has counted 9,795 first responders, downtown workers, residents, students and others with cancer deemed 9/11-related.

In all, more than 1,700 responders and others affected have died, including 420 of those stricken with cancer, officials said.

“9/11 is still killing,” said John Feal, an advocate for WTC responders. “Sadly, this fragile community of heroes and survivors is shrinking by the day.”

The number of cancer patients has rapidly risen since the federal program started tracking the disease in 2013.

“We get these referrals 15 to 20 times a week,” said Dr. Michael Crane, medical director of the WTC Health Program at Mount Sinai Hospital.

The increase is not surprising. Cancers have various latency periods, typically emerging years after exposure to harmful substances.

In addition, the average age of Ground Zero workers and others affected has risen from 38 to 55. Some are in their 70s.

“In an aging population, you’re going to see a rising cancer rate, no matter what,” Crane said.

But epidemiology studies have confirmed that 9/11 rescue and recovery workers have significantly higher rates of thyroid cancer and skin melanoma, which is potentially fatal, than found in the general population, and face a higher risk of bladder cancer. Non-responders have had significantly higher rates of breast cancer and non-Hodgkin’s lymphoma. Cancers raising red flags include leukemia and other blood-cell disorders, Crane said.

The growing tally of lost 9/11 heroes include FDNY Firefighter John McNamara, who died of colon cancer at age 44; veteran Firefighter Ray Pfeifer, 59, and John McKee, 49, a top CUNY official who joined the search-and-rescue efforts.

The living cancer victims face an ongoing struggle.

When the first plane struck, then-NYPD Sgt. Tom Wilson raced from the 90th Precinct in Brooklyn to man the Williamsburg Bridge as people fled Manhattan on foot. In the coming months, Wilson worked 344 hours at Ground Zero, sometimes sleeping at the site, and at the Fresh Kills landfill, where workers sifted debris for remains.

Wilson soon developed gastrointestinal and sinus problems, but was struck with an aggressive tongue cancer in 2008. Memorial Sloan-Kettering doctors cut off a third of Wilson’s tongue, replacing it with a skin graft from his wrist. Six weeks of head and neck radiation damaged blood vessels in his jaw, causing it to slowly deteriorate.

Now in frequent pain, he told The Post, Wilson will eventually need a reconstructed jaw, using a bone from his leg or shoulder.

But the father of five, who left the NYPD for the Suffolk County Police closer to home, is grateful to be alive — and has not lost his passion for public service.

“I probably could go out on disability, but working is my therapy — it helps me,” Wilson said. “God forbid there’s another 9/11, I want to be able to respond to that.”

Debbie Morales, then a 23-year-old receptionist for the National Coffee Association, stepped out of the subway to mayhem as the Twin Towers burned. “There are things I saw I can never undo,” she said, sobbing.

Over the next few weeks, Morales spent hours at a time in her wrecked office, retrieving paperwork for colleagues. “I had dust all over me.”

Eight years later, Morales noticed she could not understand what a TV reporter was saying. Then, she suffered two seizures at work. She was diagnosed with advanced brain cancer, and underwent an eight-hour surgery to remove most of a tumor.

Married and hoping to have kids, Morales delayed chemotherapy to go through a process to harvest and freeze some of her eggs. But complications blocked the procedure, crushing her dreams.

“I’m fearful about everything since 9/11. I was never like that before,” she cried. “I feel that thing just took everything away.”