Callinan, 30, played 32 games and kicked 49 goals for the Crows in three seasons after being given his first AFL opportunity at the 2011 rookie draft. He was elevated to the primary list at the end of last season.
Joyce, 20, was drafted at the end of 2011 but did not play an AFL game in two seasons.
Adelaide's list development and strategy manager David Noble thanked the pair for their contribution to the club and wished them well.
"In particular, I'd like to congratulate Ian, who refused to give up on his AFL dream and thoroughly deserved his chance to play at the highest level, even if it did come much later than he had hoped," Noble said.
"His contribution on and off the field was much appreciated and valued."
Callinan and Joyce join Bernie Vince (traded to Melbourne), Graham Johncock (retired) and rookies Tim McIntyre, Dylan Orval and Tim Klaosen (delisted) as departures from Adelaide's 2013 squad.
Small forward Eddie Betts (from Carlton) and key forward James Podsiadly (Geelong) joined the Crows via trades.
The Crows ended their statement saying they may still delist more players ahead of the final two list lodgements.
