Graveman was optioned to Triple-A Nashville on Tuesday.
While he held his own in a spot start last week, Graveman is no longer needed in the big-league rotation with Trevor Cahill (elbow) expected to return from the disabled list Wednesday. The 27-year-old has proven he can be an effective major-league starter in the past, so Graveman could find his way back in the big-league rotation if he pitches well with the Sounds and Brett Anderson and Andrew Triggs continue to struggle for the A's.