Tim Tebow is the biggest name among NFL cuts for the second time in three years.

Tebow had seemingly won the No. 3 QB job when Philadelphia traded Matt Barkley to Arizona on Friday.

But coach Chip Kelly cut the unconventional quarterback who showed improved accuracy since his first stint in the NFL.

“We felt Tim has progressed, but we didn’t feel he was good enough to be the (No.) 3 right now,” Kelly said.

Tebow last played in a regular season game in 2012 with the Jets, who traded for him a day after Peyton Manning went to Denver. The Patriots cut Tebow in 2013 when he failed to win a job as Tom Brady’s backup, and Tebow spent last year in the broadcast booth.

Tebow finished the preseason 21 of 36 for 286 yards, two TDs and one interception. He also ran for 82 yards and a score.

“He really improved his throwing motion from when he was throwing a couple of years ago,” Kelly said. “He worked extremely hard on it and deserves a lot of credit for that.”

Just not a roster spot.

Tebow was among more than 700 players cut across the NFL on Saturday as teams trimmed their rosters to 53.

Other quarterbacks who were jettisoned were veterans Matt Cassel (Buffalo), Rex Grossman (Falcons) and Matt Flynn, who hopes to return to the Jets after Week 1, when his salary wouldn’t be guaranteed.

“For now, it’s #bloodymary time,” Flynn tweeted along with a photo of a cocktail garnished with celery, olives and two strips of bacon.

One quarterback who isn’t looking for work is Robert Griffin III, who lost his starting job in Washington to Kirk Cousins in the preseason but not his roster spot.

Other notable players whose phones buzzed with that dreaded call to turn in their team-issued tablets included:

-WR Reggie Wayne, who caught two passes in the preseason after joining the Patriots in mid-August.

-DL Darnell Dockett after the 49ers gave him $2 million guaranteed.

-MLB Jameel McClain, who led the Giants last year with 117 tackles.

-Bengals DT Devon Still, whose daughter Leah’s cancer went into remission this spring.

-RB Jonas Gray, who never got out of Bill Belichick’s dog house after oversleeping and missing practice a few days after his 199-yard rushing performance against Indianapolis last season.

-WR James Jones, who was cut by the Giants but should draw interest, particularly from his former team, the Packers, who lost Jordy Nelson to a season-ending knee injury last month.

-Titans WR Hakeem Nicks, a former first-round draft pick of the Giants who played in Indy last season.

-DE IK Enemkpali, who gained infamy by breaking Jets QB Geno Smith’s jaw last month but got released by the Bills.

-Veteran K Nick Novak, released by the San Diego Chargers after being beaten out by rookie Josh Lambo.

The Texans cut three “Hard Knocks” favorites: CB/RB Charles James, OLB Kourtnei Brown, whose 69-yard pick-6 against Denver failed to keep him from getting released from his sixth NFL team, and WR EZ Nwachukwu.

For all the noteworthy cuts, there were some pretty prominent keeps Saturday.

Former Australian rugby league star Jarryd Hayne made the 49ers’ roster. The 27-year-old rookie return man made good on his goal nearly a year after leaving his old sport to chase his NFL dream in a quest that captivated his homeland 7,000 miles away.

Ex-Raiders quarterback Terrelle Pryor made the Browns’ roster as a wide receiver despite catching zero passes in the preseason, and the San Francisco 49ers kept linebacker Ahmad Brooks, who’s facing a misdemeanor sexual battery charge, on the active roster.

Yale running back Tyler Varga made the Colts roster, the 17th consecutive year Indy has kept an undrafted college free agent on its 53-man roster. The next two longest streaks – Kansas City (12 years) and Denver (11) – both ended.

The cruelest cuts actually come Sunday, when teams scouring the waiver wire find a better fit for their roster and jilt a player who just celebrated surviving the “final” cut down.

“It’s always fluid,” Broncos GM John Elway said. “It’ll be fluid throughout the season.”

by ARNIE STAPLETON, AP Pro Football Writer