Cleveland also announced that Sandy Alomar will stay with the team to be new manager Terry Francona's bench coach.
Jimenez went 9-17 with a 5.40 ERA in 31 starts last season. The right-hander has been a major disappointment since he was acquired in 2011 from Colorado for top pitching prospects Alex White and Drew Pomeranz.
Hafner had another injury-shortened season. He batted .228 with 12 homers and 34 RBIs in 66 games.
Hernandez's season was delayed because of false identity charges in the Dominican Republic. Formerly known as Fausto Carmona, he went 0-3 with a 7.53 ERA in three starts. Hafner and Hernandez are both eligible for free agency.
Francona was chosen over Alomar to replace Manny Acta as Cleveland's manager after the Indians went 68-94. Alomar spent last season as the Indians bench coach before being named interim manager for the final six games after Acta was fired. Alomar could be a candidate for other managerial openings, but for now he will be Francona's top coach. Next season will be Alomar's fourth on Cleveland's staff.
Francona also hired former Houston manager Brad Mills as his third base coach. They previously worked together in Philadelphia and Boston, and Francona and Mills were teammates with Montreal. Mills managed the Astros for three seasons.
Mike Sarbaugh will coach first base for the Indians. He managed Triple-A Columbus the past three years.
Information from The Associated Press was used in this report.