Glory terminated the contracts of Ecuadorian defender Luis Canga and Colombian forward Cristian Caicedo by mutual consent last week.
On Saturday it was Amini's turn, with Glory terminating his contract with immediate effect.
As part of a brief three-sentence statement on Amini's departure, Perth said they would not be making any further comment at this time.
The former Socceroos midfielder has endured an injury-plagued run since joining Glory in 2022, with a serious back issue his major obstacle.
He played 19 games in his first season with the club and 17 the next, but he's yet to feature this campaign after being grounded by a knee ailment.
The 31-year-old notched eight caps for the Socceroos between 2017-19, but his career is now at the crossroads following a lengthy run of injuries over the past year.
His most recent match was on April 28 last season, when Glory suffered a 7-1 hammering from Sydney FC.
Perth's fortunes haven't turned around under new coach David Zdrilic, with the club posting just a win and two draws from 10 games this season.
Glory were thumped 3-0 by Macarthur on Friday night, but their victory over Brisbane a week earlier at least snapped their winless run at 18 matches.
The three recent player departures frees up space for new recruits ahead of January's transfer window.
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