"This is a disappointment," Jones said in a statement released by the team. "We have been clear with Randy about what his responsibilities are and what is expected of him. This is something that he is going to have to work through and correct."
Gregory failed three drug tests during the season, and tested positive for marijuana at the NFL Scouting Combine in 2015. He slipped out of the first round before the Cowboys took a gamble on the talented pass-rusher with the 60th-overall pick.
The Cowboys appear to be willing to work with Gregory going forward, and will not cut their losses with the second-year player. After struggling through an ankle injury, Gregory recorded 11 tackles and no sacks in his rookie year.