Smith signed a five-year, $64-million contract extension in August 2019 and is still owed $7.2 million for this season, according to ESPN's Adam Schefter.
The Cowboys tried to find a trade partner before opting to cut the linebacker, a source told NFL Network's Mike Garafolo.
The 26-year-old made the Pro Bowl in 2019, but he's struggled to maintain that form since. He lost his starting role this campaign after Dallas drafted Micah Parsons in the first round and signed Keanu Neal.
Smith produced 18 tackles over four appearances (two starts) this season.
The Cowboys selected Smith in the second round of the 2016 NFL Draft. He was projected to be a first-round pick before suffering a torn ACL and LCL during the Fiesta Bowl.