In his first start of the season, Stewart gave up six runs on nine hits in 5 2/3 innings on Monday in a 12-3 loss to the Chicago Cubs. He is 1-2 with a 6.00 ERA in 18 games this season.
Axelrod, who made three appearances with the Sox earlier this season, was 5-4 with a 3.18 ERA with 66 strikeouts in 68 innings at Triple-A Charlotte.
“He’ll be the long guy, he’ll be in the bullpen,” manager Robin Ventura said of Axelrod. “Maybe a little bit down the road if something else happens, he might be able to spot start on occasion.”