To take Thornton's place, the Yankees signed lefty Rich Hill to a Major League contract, and he faced one batter Tuesday, hitting Ezequiel Carrera in the 11th inning of the Yankees' 4-3 loss in 12 innings.
"This is about giving us some flexibility in the near term because of what's going on in our starting rotation with injuries, and in the long term as we enter next year with a lot of the choices we feel are starting to knock on the door," said Cashman, who indicated he had 48 hours to mull over the Nationals' bid.
Thornton was 0-3 with a 2.55 ERA, allowing seven earned runs in 24 2/3 innings. He hadn't allowed a run in 27 of his last 28 appearances. By waiving him, the Yankees will be relieved of his contract for next year, freeing up space to move up some of their Minor League pitchers.
"Obviously we've experienced a ton of injuries, and we keep having to plug that, which Matty was providing and he was doing a great job at it," Cashman said. "We also obviously have young left-handers emerging quickly that we're excited about."
Some of those young lefty prospects Cashman mentioned are Tyler Webb, who has jumped three levels through the farm system, as well as Manny Banuelos (No. 8 Yankees prospect) and James Pazos, names who could get promoted when the roster expands in September.
"We do have a number of left-handers that we're excited about moving forward, so it's kind of a perfect-storm situation," said Cashman. "It's hard to manage that left-on-left circumstance. We'll do it right now with Hill here."
Another promising young lefty Cashman mentioned was Jacob Lindgren, the Yankees' first pick in the 2014 First-Year Player Draft and ranked No. 9 on the club's prospect list. Lindgren was promoted to Double-A Trenton on Monday, and if his quick process continues, he could see time on the big league club before the season ends.
"It's an outside shot," said Cashman. "It just depends on how things continue to progress. Somebody up here is going to have to provide the opportunity of having that need below, too. He's got other people in front of him, but if you ask who we're keeping on our mind, it's him, it's Pazos, it's Webb, Banuelos is starting to string some real positive starts now with Double-A. Those are some of the names to throw out there."
According to manager Joe Girardi, Hill will be used, at least temporarily, out of the bullpen in situations similar to how Thornton was used. It means for the time being, the Yankees will still have 13 pitchers on their active roster.
"We don't want to stay at 13 pitchers," said Girardi. "It's not something we anticipate doing for the rest of the year, and those multiple-inning guys become even more important."