In a large food processor, combine half of the chopped apricots, the yogurt, and honey. Cover and process until smooth. (If using a blender or smaller food processor, do this step in two batches.)
Pour into a 2-quart freezer container. Stir in remaining chopped apricots. Cover and freeze about 4 hours or until firm.
Chill the mixer bowl for a heavy, stand electric mixer. Spoon the frozen mixture into the chilled mixer bowl. Beat with a heavy, stand electric mixer on medium speed until slightly fluffy, starting slowly and gradually increasing the speed. Return mixture to freezer container. Cover and freeze about 6 hours or until firm.
Let frozen yogurt stand at room temperature for 20 minutes before serving. If desired, garnish with sliced apricots and/or mint sprigs.