Sam, who joined the team on Sept. 3, spent the first seven weeks of the season on the 10-man practice squad and never made it to the 53-man roster.
He thanked Cowboys owner Jerry Jones for the chance.
"I want to thank the Jones family and the entire Cowboys organization for this opportunity, as well as my friends, family, teammates, and fans for their support," Sam said via Twitter.
"While this is disappointing, I will take the lessons I learned here in Dallas and continue to fight for an opportunity to prove that I can play every Sunday."
The first openly gay player in the NFL, Sam was picked by the St. Louis Rams in the seventh round of the draft in May. When he was cut by the Rams in late August, the Cowboys picked him up and immediately placed him on the practice squad.
Sam was the Southeastern Conference Defensive Player of the Year as a senior at Missouri. However, at 6-foot-2 (1.88-m), 260 pounds (118-kg), he was seen by some as too small to play defensive end in the NFL but not athletic enough to play linebacker.
Every NFL team has a 10-member practice squad that helps it prepare for games. When injuries force players to the sidelines, the teams often look to the practice squad to fill out their game-day rosters as short-term help.
The Cowboys' decision to waive Sam, who is free to sign with another team, opens a spot for linebacker Troy Davis, a second-year pro from Central Florida who worked out with the team on Monday.