Grant joined the Cavaliers as assistant general manager in July 2005 and was made general manager June 4, 2010.
Since then Cleveland has gone 61-136, including a 16-33 mark this season.
Only three teams have worse records in the NBA Eastern Conference.
"This has been a very difficult period for the franchise," Cavaliers majority owner Dan Gilbert said. "We have severely underperformed against expectations.
"Just as this is completely unacceptable to our loyal and passionate fan base, season ticket holders and corporate partners, it is also just as unacceptable to our ownership group. I can assure everyone who supports and cares about the Cleveland Cavaliers that we will continue to turn over every stone and explore every possible opportunity for improvement to shift the momentum of our franchise in the right direction."
Gilbert thanked Grant for his service to the Cavaliers.
"Chris always conducted himself with class, integrity and was motivated by what he believed was right for the organization," he said.
Griffin joined the Cavaliers as vice president of basketball operations in September 2010 after 17 seasons in the Phoenix Suns' organization.