Mike Maccagnan just gave up on two of John Idzik’s highest draft picks.

As part of their cutdown to a 53-man roster, the Jets released 2014 second-round draft pick Jace Amaro and waived/injured Dee Milliner, their 2013 first-round pick.

They were selected by Idzik, the Jets’ general manager from 2013-14. But his successor, Maccagnan, wasn’t interested in keeping either player around.

The Jets tried to trade Milliner, the ninth overall pick three years ago, in advance of Saturday’s 4 p.m. deadline but were unsuccessful. They ultimately decided that it was better to dump the disappointing defensive back — and pay his guaranteed $2.1-million salary — than keep him as a backup. Milliner has been bothered by a hamstring injury, and if the oft-injured cornerback goes unclaimed by another team, he’ll revert to the Jets’ injured-reserve list.

Hours before the deadline, the Jets cut 20 players and placed defensive tackle Sheldon Richardson on the suspended list. He’s eligible to return to the team after their Week 1 game against Cincinnati.

After making the Amaro and Milliner moves official, the Jets placed injured right tackle Breno Giacomini (back) on the reserve/PUP list. After spending all of training camp on the active/PUP list, Giacomini will miss the first six games of the regular season.

Fullback Tommy Bohanan, a 2013 seventh-round pick, was released along with veteran receivers Kenbrell Thompkins and Jeremy Ross.

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Amaro never saw his release coming. Like another former second-round pick before him — receiver Stephen Hill — the third-year tight end was surprised by questions about his job security after playing in the fourth and final preseason game.

“I think I’ve done what they’ve asked me to do in the passing game,” Amaro said after the Jets’ 14-6 loss in Philadelphia on Thursday night.

“Obviously, catching the ball out here is different than practice — I haven’t played in so long. Getting the ball and handling it, it’s just getting that back and getting the feel of it. I felt better out there today. I’ve never really been concerned about making the roster.”

But instead of keeping him, the Jets chose to make Kellen Davis and Brandon Bostick their current 1-2 punch at the position. They also released Zach Sudfeld and Wes Saxton.

Amaro, a former star at Texas Tech, set an FBS record for yardage by a tight end with 1,352 yards on 106 receptions in 2013. Shortly after being drafted 49th overall by the Jets, he made it known that he should have been the first tight end off the board — not Eric Ebron, who was the Lions’ pick at No. 10.

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Like Hill, though, Amaro failed to live up to the hype in the NFL. After catching 38 passes for 345 yards and two touchdowns in 14 games as a rookie, he suffered a season-ending shoulder injury in the 2015 preseason opener.

In the spring, he cut out drinking and late nights and reported for the team’s offseason program expecting to be a major contributor. But his progress in training camp was hampered by a recent groin injury and he failed to impress the coaching staff enough.

After Idzik traded away star cornerback Darrelle Revis days before the 2013 draft, he took Milliner as his first-ever pick. Now, three years later, Milliner is gone — and only seven of the 19 draft selections from the Idzik era currently are on the Jets’ roster.

Milliner, 24, has dealt with an assortment of ailments since making it to the NFL, including a wrist injury that required surgery and a torn Achilles tendon last year. And his offseason progress was slowed by biceps and hamstring injuries.

He ends his Jets career with three interceptions, 19 passes defensed and 68 tackles in 21 games.