Reserve outfielder Michael Ryan and backup infielder Brent Abernathy were removed from the Twins' 40-man roster along with Rivas. All are likely to become free agents.
As the club broke Spring Training with a mostly revamped infield, the 26-year-old Rivas was expected to provide stability as its lone experienced veteran, but he faltered early before eventually being demoted to Rochester on July 16.
The move was expected for Rivas, who avoided arbitration last winter when he signed a one-year contract worth $1.625 million. The cost of keeping him in 2006 would have escalated had he gone through arbitration this offseason.
Rivas, a .262 lifetime hitter, was signed as a 16-year-old out of Venezuela and was one of the organization's promising stars when he reached the Major Leagues in 2000. In 2001, he set a rookie record by notching 31 stolen bases and was heralded as one of the league's best at turning the double play.
But Rivas often drew criticism from coaches, including manager Ron Gardenhire, for not improving enough and for a lackadaisical approach both at the plate and defensively. After demoting Rivas in July, Gardenhire said he hoped it would provide the infielder with a "wake-up call." He was only brought back as a September callup after rosters expanded.
"We tried different approaches, it just wasn't happening," Ryan said. "Maybe it's best to sever and go our separate ways."
Ryan batted .231 in 57 games this season with two homers and 13 RBIs, while splitting time between the Majors and Rochester. He hit his five other career big-league homers during one month as a late-season callup in September 2003, but battled with his confidence and often struggled offensively since. Minnesota selected Ryan as its fifth-round pick in 1996.
Abernathy, 28, was a non-roster invite to Spring Training and joined the Twins in June during the first of two callups this season. He batted .239 in 24 games playing second base and left field.
Ryan said there was a chance Abernathy could return to the organization if a new deal could be worked out.
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.