Both players will remain with the club this road trip as part of the Astros' five-man taxi squad, which also includes catcher Michael Papierski.
Abreu had been a highly-regarded prospect coming into the season who was expected to play a key role on the staff, either in the bullpen or as a spot starter.
His four appearances so far, however, have not been impressive.
Abreu walked seven of the 20 batters he faced and threw just 30 strikes in 76 pitches.
Astros manager Dusty Baker said Abreu had been thinking too much on the mound. Abreu also arrived to summer camp out of shape, Baker said.
Combining those two issues is likely what led to his less than stellar performances..
Mayfield is a solid backup infielder, but with the Astros' health issues in pitching, that was positional depth they sacrificed.
Baker said pitcher Jose Urquidy, who had been projected as the No. 4 starter in spring training but was unable to attend summer camp, is throwing off a mound in Corpus Christi.
Reigning American League Rookie of the Year Yordan Alvarez, who also was unable to attend summer camp, is taking batting practice and running in Corpus.
Still, Baker said reinforcements from players dealing witht health issues are still "a long way off."
The Astros face the Arizona Diamondbacks on Thursday night in a rubber match at Chase Field.