Captured killer David Sweat gave cops a blow-by-blow of his escape and time on the run with fellow fugitive Richard Matt — revealing that their original plan was to flee to Mexico with the help of Shaw-skank prison worker Joyce “Tillie” Mitchell.

Sweat claimed the lovestruck sewing-shop supervisor, who is charged with smuggling tools to the convicted killers, was the only other person who knew of their elaborate breakout plan, sources said on Monday.

Sweat — who a source said was “spilling his guts” to investigators — said he and Matt planned to drive to Mexico in Mitchell’s car following their June 6 escape.

He said Matt, who had the words “Mexico Forever” tattooed on his back, came up with the idea of heading south of the border, boasting of connections he made while serving time for a fatal stabbing there, sources said.

“They would kill Mitchell’s husband and then get in the car and drive to Mexico on the theory that Mitchell was in love with one or both of them,” Gov. Andrew Cuomo said.

“Then they would go live happily ever after — which is a fairy tale that I wasn’t read as a child, but we will believe what we want to believe.”

When Mitchell got cold feet and failed to show up, however, the escapees had to improvise and decided to head to Canada.

Sweat, 35, told cops he and Matt, 49, broke into a series of hunting camps and cabins they used as hideouts and ransacked for weapons, food, clothing and other supplies, sources said.

The loot included a transistor radio they used to follow news accounts and avoid the manhunt that grew to involve more than 1,000 local, state and federal law enforcement personnel.

They also found liquor and pot that Matt eagerly consumed, slowing their progress — which was already impeded because the older man suffered from sciatica and bloody blisters, sources said.

Sweat said he got fed up and decided to ditch Matt about five days before he was captured.

Sweat was carrying a compass, along with water, Pop-Tarts and a can of Vienna sausages when he was shot twice in the torso and caught by State Police Sgt. Jay Cook a mile and a half from the border Sunday afternoon.

He’s being treated at the Albany Medical Center, where his condition was upgraded from critical to serious on Monday. He will be charged with escape and burglary, Clinton County DA Andrew Wylie said.

Matt was fatally shot three times in the head by a federal agent Friday when he refused to drop a stolen 20-gauge shotgun, according to authorities.

He had sardines with him when he was killed, sources said.

Sweat told cops that he and Matt had plotted their escape through underground steam tunnels for months, but didn’t put the plan into action until May, when the heat was turned off at Clinton Correctional Facility in Dannemora, sources said.

Sweat admitted doing most of the cutting and other heavy work because he was in better shape than Matt, sources said.

His confessions spanned several hours following his arrival at the Albany hospital, and authorities plan to continue questioning him, sources said.

A doctor at the hospital said Sweat was being treated on a “locked-down” floor, with dozens of cops and security guards standing watch.

“I heard he was only capable of mumbling and gurgling noises last night because he was under extremely heavy sedation. Now he’s spilling his guts to the police,” the physician said.

Broome County Sheriff David Harder told The Post that Sweat picked up outdoor skills in his youth when he took part in a program intended to keep him from a life of crime.

“He had problems as a juvenile. They tried to save him,” Harder said. “So he took some kind of a class or training on how to survive in the wilderness.”

Law enforcement sources said Sweat would not be sent back to the Dannemora lockup following his recovery, and would likely end up in Sing Sing, just north of New York City, or another maximum-security prison.

“His privileges will be extremely limited,” Wylie told CNN. “He will be, you know, basically [under] 24/7 lockdown for the rest of his life.”

Meanwhile, sources said the FBI has launched an investigation of drug-trafficking and other criminal activity at Clinton Correctional, based on information developed during the initial round of interviews conducted following Sweat and Matt’s escape.

The federal probe follows Cuomo’s order that the state Inspector General’s Office conduct a top-to-bottom investigation of the jailbreak with the help of an independent expert.

Other investigations are being conducted by the State Police and the Clinton County DA’s Office.

“Agents are reinterviewing inmates and prison workers who have already been interviewed by state investigators,” one source said. “This is a vote of no confidence by the feds in the state investigation.”

Also Monday, Clinton Correctional Officer Gene Palmer appeared briefly in court on charges he provided tools to Sweat and Matt, and destroyed several paintings that Matt gave him.

Palmer, who is free on bail, waived his right to a preliminary hearing through his lawyer and said nothing either in court or outside.

Additional reporting by Frank Rosario