The Yankees also designated Jones for assignment on July 31 after acquiring infielder Dustin Ackley in a trade with the Mariners, but they re-signed Jones when Ackley was placed on the disabled list with a right lumbar strain. This most recent cut would make it tougher for Jones to return.
"Two times in a row, it's a little different feeling than last time," Jones said. "I just have to weigh the options and see. There could still be an opportunity here to help the team win. I enjoy being here, I like the guys and I enjoy the clubhouse and the coaching staff and everybody.
"That aspect of it is tough to leave, but in the scheme of things, I have to think of my career and the chance to play and what's best for that."
If he clears waivers, Jones could refuse an assignment to the Minors and become a free agent. Yankees manager Joe Girardi said that it was difficult to have that same conversation once again with Jones in the wake of Tuesday's 5-4, 16-inning loss at Cleveland.
"If we're not in a game like yesterday, it probably doesn't happen," Girardi said. "If we're not in a game like yesterday or we're in a 16-inning game and you have plenty of pitching today, maybe he even plays today. But we felt that we needed to get some more pitching here and make sure that we're covered for the next few days, and it was really difficult."
Capuano is 0-4 with a 6.97 ERA in 16 appearances, including four starts, for the Yankees this season. Goody made two appearances for the Yankees earlier this season. The 24-year-old is 1-1 with a 1.64 ERA in eight appearances for Scranton/Wilkes-Barre this year.
Jones, 34, was hitting .215/.257/.361 with five homers in 57 games, but at-bats were scarce because both Mark Teixeira and Alex Rodriguez have been healthy and productive for most of the season. Jones had not appeared in a game since re-signing with the organization on Aug. 5.
"I wasn't able to get the at-bats I thought I was going to be able to get," Jones said. "It is what it is. I was very happy to be a part of this team and organization, but career-wise and baseball-wise, from my standpoint, the at-bats weren't there and playing time wasn't there. It's understandable, of course."
Pinder (0-2, 3.12 ERA) picked up the loss in Tuesday's 16-inning game, allowing one run on three hits in 1 1/3 innings.