Nelson managed 102 games for the Eagles after being drafted with pick 51 in the 2014.
Dixon and Joyce were recruited as supplementary selection period players when West Coast was being hit by an almost unprecedented injury crisis in the pre-season.
Former Fremantle forward Dixon played 10 games this season while an ankle injury kept Joyce from stepping foot on-field at any level in 2022.
Football Manager Gavin Bell thanked the players for their contribution to the club.
“Jackson, in particular, has made a long and strong contribution to our club,” Bell said. “He has been a popular member of our playing squad for eight seasons, including two Grand Final campaigns.
“Along with Hugh and Tom, who answered an SOS call from the club in the pre-season, we wish each of them every success for next phase of their lives and in football.”