The Miami Herald, citing two sources it did not identify, said Martinez tendered his resignation before Sunday's game against Pittsburgh after Marlins owner Jeffrey Loria rejected an earlier offer to resign.
Team officials later confirmed to MLB.com Martinez had been replaced by field director John Pierson on an interim basis.
The former New York Yankees World Series hero was accused by rookie second baseman Derek Dietrich of grabbing him by his neck and neck chain in alleged incident several months ago, two unnamed sources told the Herald.
The newspaper said other players -- including outfielder Justin Ruggiano, infielder Chris Valaika and minor-league infielder Matt Downs -- claim to have been subjected to profanity-laced tirades from Martinez since his hiring before spring training.
Dietrich's agent wouldn't comment, while a Marlins official neither confirmed nor denied the club had been investigating any alleged abuse, the Herald said.
The sources said the Major League Baseball Players' Association and the MLB commissioner's office had been informed of the alleged incidents.
Martinez, 45, spent 16 years in the major leagues, mostly with the Yankees and Seattle Mariners.