Hawksworth never pitched in 2012, undergoing three operations, two to his right elbow and one to his right shoulder. The 29-year-old, obtained from St. Louis for Ryan Theriot two years ago, would have been eligible for salary arbitration.
The 27-year-old Angle was claimed off waivers from Baltimore in February as insurance in the event of injuries, but was never called up to the Major Leagues. He had a solid season at Triple-A Albuquerque, hitting .303.
The Dodgers will be making numerous roster moves in the coming weeks, as they have 46 players under control, including 11 that finished the season on the disabled list.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.