Andrews, 30, will leave at the end of the season after two years in England while John, 33, has spent six seasons with Sale across two spells.
Also leaving at the end of the campaign are prop Tumy Onasanya, back-row Huw Davies, scrum-half Nye Thomas, wing Albert Bradshaw, centres Tom Curtis and Joe Bedlow and academy players Tom Davis and Frank Chatterton.
The club have also confirmed that Irish hooker Tadgh McElroy, centre Sam Bedlow, second-row Rouban Birch, scrum-half Will Wootton and prop Jack Lightbown have left with immediate effect.
