Lock Gulliver was recruited from Cornish Pirates at the start of the season and made 13 appearances for Warriors, including five in the Aviva Premiership. Gulliver scored tries both home and away against Banca Monte Crociati this season.
Samoa international Muagututia joined the Warriors in September and has made six first team appearances in the LV= Cup and Amlin Challenge Cup.
Head Coach Richard Hill said: "Both Tom and Ben have been unfortunate in that the opportunities they have had this season have been limited by the form and consistency of players in their respective positions. We wish them both well in the future and thank them for their efforts at Sixways.
"We believe that Richard could yet have a bright future, but it is crucial he gains more game time and so hopefully we can help him secure a club in the RFU Championship and develop his game. He has been a good member of the squad, extremely popular and so we also thank him for his time at Warriors."
Worcester have already confirmed that Marcel Garvey, Miles Benjamin, Alex Crockett, Bruce Douglas, Oliver Tomaszczyk, Dale Rasmussen, Kai Horstmann, Chris Fortey, Sione Tu'ipulotu and Mike Penn will all leave the club at the end of the current campaign.