The 24-year-old has had no setbacks or soreness this spring, but needs more work than he would get with the Braves.
The team had considered using Boyer as a starter at Richmond, but Cox said that the right-hander would pitch out of the bullpen on some form of a regular schedule.
Boyer will likely work at least two innings per appearance in the International League, allowing him to work on all his pitches.
The Georgia native needed just six pitches in a 1-2-3 seventh inning against the Indians on Saturday in Winter Haven.
In five Grapefruit League appearances, Boyer is 1-0 with a 1.29 ERA. He allowed four hits in seven innings, striking out three and walking four.
"He just needs to build himself back up," Cox said. "His arm is great. He's been impressive."
That's what Boyer had also been as a rookie in 2005. Called up from Double-A Mississippi in early June, he was 4-2 with a 3.11 ERA in 43 appearances. He struck out 33 in 37 2/3 innings, and opponents batted just .234 against him.
Roster at 37 players: The Braves also sent outfielder T.J. Bohn to Triple-A Richmond, reducing the roster to 37.
Cox said that no more cuts are expected before the team heads to Atlanta for a pair of exhibition games against the White Sox next weekend.
Bohn, 27, was claimed off waivers from the Mariners last November. The right-handed hitter had 14 at-bats with the Mariners in 2006, with one of his two hits a home run.
The Braves were impressed this spring with the 6-foot-5 Bohn's defense.
"He can play center field," Cox said.
Bohn hit .222 in Grapefruit League play, with two doubles and five RBIs.
Yates fighting for a spot: The Braves still have 17 pitchers in camp, with decisions on the fifth starter and the last couple of spots in the bullpen still to be made.
Reliever Tyler Yates knows he hasn't helped himself with his performance so far.
"But I should get three more chances," the right-hander said. "Hopefully, they'll all be good."
Yates, who is out of options, has given up runs in each of his past three appearances, including a two-run homer by Cleveland's Ryan Garko in a 4-3 loss on Saturday.
The shaky outings have lifted Yates' ERA to 5.62, but he insists he isn't discouraged.
"I actually think that I've pitched better than in my first couple of games," Yates said.
Cox certainly hasn't written Yates off.
"I really like his stuff," the manager said.
The 29-year-old revived his career with the Braves last season, pitching in 56 games and posting a 3.96 ERA.
Chipper goes deep: Chipper Jones has certainly felt no after-effects since missing five games with a strained right oblique.
The third baseman has homered in each of the past two games and is 5-for-11 since returning. All but one of the hits have been for extra bases.
"I feel good," Jones said. "Now, I have to keep it that way."
Jones' homer on Sunday, hit from the right side off Nationals rookie Matt Chico, was a massive shot to center field that hit high off the batters' backdrop at Disney's Wide World of Sports. His homer on Saturday against the Indians at Winter Haven was hit from the left side.
Jones is batting .333 for the spring, with three homers and nine RBIs.
Pitching sharp again: The Braves' 6-0 victory over the Nationals was their second shutout of the Grapefruit League season. They have the second-lowest ERA among National League teams, behind only the Cardinals.
Chuck James (3-1) lowered his ERA to 1.80, limiting the Nationals to two singles over six innings. He struck out four and walked four in his second consecutive scoreless outing.
"He looked good again," Cox said.
Bob Wickman, Rafael Soriano and Macay McBride followed James, with Soriano striking out the side in the eighth inning.
"Soriano's been perfect all spring," Cox said.
Acquired from the Mariners for Horacio Ramirez, the right-hander has a 1.12 ERA and 12 strikeouts in eight innings.
Coming up: The Braves will play the Astros on Monday in Kissimmee at 1:05 p.m. ET. Lance Cormier, who is 3-0 with a 1.29 ERA in the Grapefruit League, will start for the Braves against Woody Williams.