Miami manager Mike Redmond said control issues and an inability to throw multiple innings prompted the decision. The 27-year-old right-hander struck out 14 and allowed six runs in nine innings this spring.
"I hope we are able to keep him in the system and build him up," Redmond said.
Rodriguez, signed as a free agent, is 5-7 with a 4.24 ERA in a five-year career with the A's, Nationals and Cubs.
Miami optioned outfielder Jake Marisnick and infielder Donovan Solano to Triple-A New Orleans and reassigned pitcher Chris Hatcher, outfielder Matt Angle and infielders Juan Diaz and Austin Nola to the minors.
The 22-year-old Marisnick hit .432 in 44 spring training at-bats and stole four bases.
"That was a tough one," Redmond said. "There's no doubt that this guy is the center fielder of the future for us."