Preheat oven to 450°. In the bowl of a food processor, combine flour, baking powder, butter, shortening, and salt, and pulse several times until mixture resembles coarse meal. Pour in milk and pulse just until dough is blended. Drop heaping mounds, about 2 tablespoons each, 2 inches apart on an ungreased baking sheet. Bake 12 to 14 minutes until golden. Cut each biscuit horizontally into 3 slices. (Can be made 1 to 2 days in advance.)
Line four to six 6-ounce teacups with plastic wrap—allow a 3- to 4-inch overhang on each side. Pour 1 tablespoon berry puree in the bottom of each teacup. Top with a layer of biscuit. Repeat layering 2 more times. Pour any additional puree over top, allowing it to seep into biscuit. Wrap trifle with plastic wrap, sealing tightly. Refrigerate 1 hour or overnight.
To unmold, unwrap plastic wrap and turn teacup over onto a plate. Garnish with remaining 1/4 cup berries.