Arizona was the talk of the NFL after opening the season 4-0 but the Cardinals lost nine consecutive games before ending the season 5-11.
It was the second time in three seasons Arizona managed just five wins and the third consecutive year the Cardinals missed the playoffs.
Graves had been with the organization since 1997 and was named general manager in 2007. Whisenhunt was hired as head coach for the 2007 season. After going 8-8 that season, the Cardinals advanced to Super Bowl XLIII, losing to Pittsburgh.
Arizona returned to the playoffs in 2009 but the slide started the following season.
Team President Michael Bidwell fired most of the coaching staff on the offensive side of the ball, along with Whisenhunt and Graves.
Defensive coordinator Ray Horton was retained and is expected to be considered for the head-coaching vacancy.
'Happy' fan videos make Pharrell cry [VIDEO]
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend