The team also selected the contract of outfielder Collin Cowgill from Triple-A Reno.
Putz missed 19 games with elbow tendinitis after being placed on the disabled list on July 1, retroactive to June 29. He was 1-2 with 21 saves and a 3.12 ERA in 34 games. David Hernandez has pitched well in Putz's absence, leaving the Diamondbacks with a tough decision now that he's back.
Blum broke his finger while fielding a ground ball against Colorado on Sunday, less than a week after being activated from the DL with a knee injury.
Cowgill .hit 354 with 13 homers and 70 RBIs at Reno.