Acosta appeared in six Grapefruit League games, giving up four earned runs in seven innings (a 5.14 ERA) with 10 strikeouts and five walks.
If Scott Proctor (elbow surgery) isn't ready for Opening Day, the Braves seem to have two bullpen spots left. And with Acosta gone, the front-runners are right-handers Jesse Chavez and Craig Kimbrel and left-handers Jonny Venters and Jo-Jo Reyes.
The 28-year-old Acosta has posted a 3.55 ERA spanning 103 relief appearances through three seasons with the Braves. Last year, his ERA was 4.34 in 36 games.
"We're running out of innings," Braves manager Bobby Cox said.
Atlanta is expecting to make more cuts on Sunday and Monday.
Alden Gonzalez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.Less