Peel, quarter and core apples. Dice them coarsely and combine in a 4 quart saucepan with the apple juice concentrate. Bring juice to a boil. Turn heat to simmer, cover and cook for 10 minutes. Add blackberries. Return the heat to simmer, cover and cook for 5 minutes. Uncover the pot. Turn heat up to medium high and reduce the liquids. Cook until a spoon drawn across the bottom of the pan causes a hissing sound. This will happen within 10 minutes.
Remove jam from the heat. Crush the mint and add to the hot jam. Steep for 5 minutes or until the mint scant is noticeable. Remove mint and spoon the jam into hot, sterilized jars and screw clean caps on tightly. Process in a boiling water bath (with water covering the jars 1 inch over the tops) for 10 minutes. Makes 3 cups.