Logan Kensing will join the team from Triple-A Syracuse.
"Julian had a lot of outings where everything that could go wrong went wrong," interim manager Jim Riggleman said. "Along with pitching not as well as he would like, he didn't get any breaks, either."
Tavarez (3-7) entered Sunday's game with two on and one out in the fourth inning. He allowed both inherited runners to score and gave up a run of his own before recording two outs to exit the inning.
Prior to Sunday, Tavarez had inherited 20 runners all season and allowed only two to come home. But his frequent bouts of wildness -- 27 walks in 35 innings -- helped lead to a 4.89 ERA.
The 36-year-old agreed with the Nationals' decision to let him go but showed no doubts that he would be back in the Majors by season's end.
"This year you will see me with someone else," Tavarez said. "Tomorrow I'm going to be running and throwing balls, waiting for someone to give me a phone call. I'll be back."
Tavarez went through this situation twice last season, and caught onto a third team -- Atlanta -- by the end of the season. The Nationals signed him as a free agent in March.
Tavarez's replacement, Kensing, was ineffective in 12 outings for the Nationals in April and May. He was 0-2 with a 13.14 ERA before being sent to the Minors.
At Syracuse, Kensing has steadied his pitching a bit. In 25 1/3 innings, he has a 3.91 ERA with an encouraging 24 strikeouts against five walks.
"He's made a lot of progress, throwing the ball really well, cutting the ball more to help him out in certain situations," Riggleman said.
Riggleman also applauded Tavarez for the character he showed with the Nationals this season.
"He's been a great influence for our younger guys," he said. "He prepared hard every day to be ready to pitch, and he took the ball many times when his arm may have been hanging a bit."
Mark Selig is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.