The Demons also upgraded defender Mitch Clisby to its senior list for 2014, after the 23-year-old played eight games in 2013.
Magner earned two Brownlow votes on his AFL debut in round one, 2012, and was a standout performer as the team lost its first nine games that season.
He played 17 games in his first season, with his form tailing off as the year went on. He then appeared to fall out of favour, playing just two games in 2013 and finishing sixth in the Casey Scorpions' best and fairest.
The 26-year-old midfielder was quick to express on Twitter that he hoped to get a second chance at another club:
"Privileged to have played AFL and still think I have something to offer. Thanks to everyone for all the support this year! #lifegoeson"
Taggert did not play a senior game after being selection No.36 in the 2011 AFL Draft. His first season was virtually wiped out by stress related injuries in his shins and back.
In 2013, Taggert played a pre-season game and was named an emergency for the round 23 clash against the Western Bulldogs but did not break into the team.
His delisting means no player selected in the 2011 draft or rookie listing remains at the club.
Stark was selected as a rookie in 2012 and joined the team on its pre-season camp in Darwin. He managed just five games in the VFL development league with his progress hampered due to knee, groin and ankle injuries.
Clisby is the only player remaining from the 2012 rookies. He made his debut in round 13 and played eight games before missing the final three rounds due to suspension.
Melbourne has now delisted Taggert, James Sellar, Troy Davis, Tom Gillies and Josh Tynan from its senior list and Stark, Magner and Tom Couch from its rookie list.
Aaron Davey, David Rodan and Joel Macdonald have also retired.