It should take just a few days for a bullied student to transfer to a safer school — but a Staten Island boy’s plight provides another example of how education bureaucrats extend bullying victims’ pain for months.

Cyon Williams, an 11-year-old honors student at IS 61 in New Brighton, waited four months for a transfer this school year.

Cyon finally dropped out this month, with a doctor’s note ­describing anxiety symptoms so bad, he’d bitten off his fingernails and had to endure an endoscopy to check his severe stomach pains. He is now in therapy.

His mom, Halcyone Williams, ran to hug Cyon when she heard last week that Noel Estevez, 14, of The Bronx, had allegedly killed one of the bullies who had made his life a living hell.

“That could have been my son,” Williams remembers thinking.

The Department of Education declined Saturday to discuss the cases, or release data on bullying incidents and safety transfers, which send bullying victims to other schools.

Like the Estevez family, Williams tried in vain for months to get staff at Cyon’s school to transfer him after the slightly built sixth-grader was terrorized by classmates.

“I was pushed and shoved,” says Cyon, who hopes to become a marine biologist. “Kids would call me gay and f–got — all these curse words.”

Cyon had to spit on his own lunch before eating it, he says, or the other boys would take it.

“Killing myself or killing others was on my mind — I couldn’t deal with it anymore,” he admits.

His mom said Saturday she’s speaking out not just for him, but for Noel Estevez and “every other child that’s going through this.”

“My school did nothing,” Halcyone said. Told of the lunch thefts, the principal allegedly smirked. “She said, ‘I don’t know why, but mozzarella sticks are a hot commodity,’ ” Halcyone ­recounted.

In April, when Halcyone went to the DOE to demand a “safety transfer,” she was asked for documents that she had never been told she would need.

“The office of student enrollment said, ‘Do you have a police report? Do you have any incident reports?’ I did eventually go to file a police report,” she said. “I went to the 120th Precinct on June 6, and filed a harassment complaint.”

When the DOE finally offered Cyon a transfer earlier this month, it was to IS 51, also in New Brighton. Halcyone wasn’t happy with the choice. “They have a social-environment rating of only a C, and other parents told me that school would be just as bad,” she said.

In the four days since Noel allegedly stabbed Timothy Crump to death, education officials have not issued any directives to principals reminding them of their obligations to deal immediately with safety complaints, noted Mona Davids of the New York Parents Union.

On Saturday, Noel’s mom, Maria Estevez, visited her son at Horizon Juvenile Center in The Bronx, saying afterward, “He’s sad. He’s hurt.”

“This system is f–ked up,” she cried. “The school didn’t do nothing. ACS [Administration for Children’s Services] didn’t do nothing. The police didn’t do nothing. Nobody did nothing for my son.”

Additional reporting by Michael Gartland and Kevin Fasick