Infielder Chris Burke, catcher Robby Hammock, lefty Wil Ledezma and outfielder Jeff Salazar became free agents as a result of the club's decision.
The D-backs signed their other salary arbitration eligible player, Augie Ojeda, to a one-year contract earlier this week.
With the moves, the D-backs 40-man roster stands at 36.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.