The 19-year-old made 10 appearances for the club and came into the first team for the first time this season for the Scottish Communities League Cup semi-final against Inverness.
Mullen looked set to play in the final but his season was ended by a broken foot suffered the previous week against Hibernian.
He wrote on his Twitter account: "Not being offered a contract for next season at hearts.
"Enjoyed being at the club since I was 12 but annoyed the way last few months ended with the injury.
"Absolute gutted at leaving some of the boys gona miss them a lot."
Hearts have previously confirmed that Danny Grainger, Darren Barr, Gordon Smith and Denis Prychynenko would not be offered new contracts, while club captain Marius Zaliukas is also set to move on as the club look to cut costs again.