Make this recipe a day ahead to allow for proper chilling.
In a medium saucepan over medium-low heat, place berries, sugar, water, jelly, and juice. Stir to combine. Bring to a simmer, stirring occasionally, until the sugar dissolves and the berries begin to release their juices, about 5 to 10 minutes. Remove from heat and cool completely. Strain fruit over a bowl, reserving both the fruit and the liquid.
Line six ¾-cup ramekins or custard cups with plastic wrap. Using a 3-inch cookie cutter (or a sharp knife to trace around the bottom of a ramekin), cut 12 rounds from the bread, reserving bread scraps. Dip six of the rounds into the reserved liquid and place in the bottoms of the ramekins. Cut any remaining bread into 1-inch strips. Individually dip strips and scraps into the liquid and line the sides of the ramekins. Place ¼ cup berry mixture into the center of each. Dunk the remaining bread rounds into the liquid and press lightly into the berries. Fold in the sides of the plastic wrap over the tops of the ramekins. Place ramekins on a baking sheet, top with another baking sheet, and put in refrigerator. Weigh down uppermost baking sheet with either heavy cans or foil-covered bricks. Refrigerate overnight.
Remove puddings from refrigerator. Unwrap, invert onto individual plates, and serve with whipped cream, mint leaves, and berries.