The source told ESPNNewYork.com that Turner's propensity for not running hard irked the front office, which had finally seen enough.
Turner, arbitration-eligible, likely was due to make less than $1 million in 2014.
He should have no trouble finding a job this offseason. Among Turner's longtime fans is Atlanta Braves manager Fredi Gonzalez.
Report: Arbitrator to make Hamilton rehab call
A-Rod singles in first spring training at-bat
Wright, Syndergaard clear air after dustup
Mets' Murphy to keep religious beliefs to self
Cobb gets start for Rays on Opening Day
Red Sox CF Castillo sidelined by oblique strain
Martinez: Common spring MLB misnomers
Arbitrator To Rule On Hamilton Rehab
"Mike & Mike" discuss the four-person disciplinary committee that is deadlocked about whether Josh Hamilton should enter rehabilitation after suffering a drug relapse; now an arbitrator will make the decision.
A-Rod Singles In Yankees' Loss
Alex Rodriguez went 1-for-2 with a walk in his first baseball game in nearly 18 months as the Phillies beat the Yankees 3-1.
Breaking Down A-Rod's First Game Back
Karl Ravech, John Kruk and Buster Olney evaluate Alex Rodriguez's performance in his first baseball game in nearly 18 months.