The incident, which took place Jan. 17 in the ship's berthing area, was captured on cellphone video.
The Navy says the eight sailors on the U.S. Bonhomme Richard assaulted and choked a new arrival as part of an initiation rite. Such acts are strictly forbidden.
One of the discharged sailors called it a friendly wrestling match, and he believes the penalty was too severe.
"Play wrestling with no malicious event, and for eight people's lives to be destroyed, you've got to be kidding me," said Davis.
None of the eight sailors decided to appeal the decision by the ship's captain to discharge them from the Navy.
The action follows recent congressional hearings on hazing in the military, including the case of Lance Cpl. Harry Lew, who shot himself in a foxhole in Afghanistan last year after he was beaten, forced to do repeated pushups and fed mouthfuls of sand.
The Associated Press contributed to this report.