Rhodes, 29, had three years left on a five-year extension he signed with Minnesota in 2017 and was carrying a $12.9 cap hit into 2020. With his release, Rhodes will count $4.8 million against Minnesota's cap in 2020 and save the Vikings $8.1 million.
The former first-round pick should have a second-chance market for his services.
Joseph, 31, also had three years left on his contract with the Vikings, but will hit free agency earlier than expected.
The veteran defensive tackle was owed $12.9 million in 2020, but his release will save Minnesota $10.5 million in cap space.
Joseph logged three sacks in 13 starts last season. Over six seasons in Minnesota, Josep played 88 games, starting all of them, and picked up 15 sacks. A Pro Bowler in 2016 and 2017, Joseph could cash in this spring.