Jackson, 28, is a career .277 hitter with 46 homers and 247 RBI but is hitting just .238 this season after an injury-plagued 2009 season in which he hit .182 in 30 games.
Demel, 24, was 9-8 with a 2.70 earned run average and 42 saves in 151 relief appearances in four years in the Athletics' minor league system. He recorded 200 strikeouts against 90 walks.
He was a third-round selection of the Athletics in 2007.
This season, he was 2-0 with six saves and a 1.26 ERA in 22 games for Class AA Sacramento.
The Diamondbacks also said infielder Tony Abreu is back from the 15-day disabled list. Abreu was hitting .313 before being sidelined by a wrist injury.