The Dominican right-handers were placed on paid non-disciplinary leave by MLB last July but were indicted on federal conspiracy charges last November in New York.
They pleaded not guilty to helping Dominican gamblers win wagers based upon the types and speeds of certain pitches.
An agreement between MLB and its players association will mean the Guardians do not have to continue paying Clase and Ortiz during the season that begins next week.
"As the legal proceedings involving Cleveland Guardians pitchers Emmanuel Clase and Luis Ortiz continue to move forward, MLB and the MLBPA have agreed that both players will remain on non-disciplinary leave from the club without pay until further notice," Major League Baseball said in a statement.
"This agreement is not an admission of any wrongdoing by Clase or Ortiz. MLB has been closely monitoring the matter since alerting federal law enforcement at the outset of its investigation and will have no further comment until its investigation has been completed."