"Joao Alves has done a fantastic job with the club and it's not without regrets that we are relieving him of his duties," the club's Canadian owner Hugh Quennec said in a statement on Servette's website.
The 17-times Swiss champions are bottom of the table with two points from eight games and last week failed to qualify for the Europa League group stage.
Alves had been in charge since April during his second stint at the club.
Quennec bought Servette in March, rescuing the club after it filed for bankruptcy under previous owner, Iranian businessman Majid Pishyar.
Sion coach Sebastien Fournier quit on Monday and has been replaced by Michel Decastel.