PHOENIX — Even before the worn-down Mets bullpen blew Monday night’s game, general manager Sandy Alderson had been working the phones, hoping to bring in a new arm.

Those efforts led to the signing of righthanded reliever Neil Ramirez, who joined the Mets on Tuesday in time to be in uniform against the Diamondbacks. He took the spot of shortstop Asdrubal Cabrera, whose existence in injury limbo finally came to an end when the Mets placed him on the 10-day disabled list retroactive to Sunday with a sprained left thumb.

The Mets’ roster reshuffling — which came amidst a five-game losing streak — shifted Jose Reyes to shortstop and added a fresh arm to a bullpen that has shown the wear for carrying such a heavy workload for a rotation that failed to pitch deep into games.

“We certainly are in need of a guy who can come out of the bullpen and has some experience down there,” manager Terry Collins said before Tuesday night’s game. “Hopefully, he’ll get some outs for us.”

Ramirez, 27, is hardly a cure-all. In nine appearances with the Giants this season, he allowed 10 runs in 10 1/3 innings (8.71 ERA), though he has struck out 18 batters while walking just four. The Blue Jays claimed Ramirez off waivers but designated him for assignment before he pitched in a game.

“Every mistake I did make was getting hit,” Ramirez said. “When I was making pitches I needed to make, I was getting guys out. The ones that were coming back across the plate and kind of up in that bad middle up area, it’s like anybody. You’re going to get hit. You just have to limit those.”

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Ramirez rejected an outright assignment to become a free agent, then hoped for an opportunity. The Mets called on Monday, and after a day spent in negotiations, Ramirez wound up back in the big leagues with his third different team since Opening Day.

“It’s definitely been a crazy couple of weeks,” said Ramirez, who has a carer 3.72 ERA in 96 appearances over the last four seasons, with most of them coming with the Cubs.

At the very least, Ramirez provides a fresh arm for a Mets bullpen that has paid dearly for a starting rotation that is averaging less than five innings per start in May.

Entering play, of the 10 National League relievers who have made at least 20 relief appearances this season, four are in the Mets bullpen. Addison Reed, Hansel Robles and Fernando Salas have each pitched in 20 games while Jerry Blevins leads the NL with 22 appearances.

As a group, Mets relievers have a 5.26 ERA, the third highest in the National League and just behind the Nationals, whose bullpen had expected to be a weakness. Opposing batters have hit a league-worst .281 against the Mets bullpen while bashing 23 homers, second most in the league.

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Ramirez hasn’t pitched in a big-league game since April 29, though he has been throwing bullpens. To make room for him on the 40-man roster, the Mets moved closer Jeurys Familia on the 60-day disabled list. He’s expected to miss three months after undergoing surgery to remove a blood clot, an injury that the Mets bullpen even more vulnerable.

Meanwhile, it’s unclear how long Cabrera will be on the shelf. He had tried to play through the pain caused by his thumb injury before reaggravating it on a swing on Saturday.

Said Collins: “Yesterday, he thought he was going to need some days to let him just finally totally heal.”