Prepare the pastry and divide in half. Form each half into a ball. On a lightly floured surface, roll one ball of the pastry into a 12-inch circle. Transfer the rolled-out pastry into a 9-inch pie plate.
In a large mixing bowl, combine the sugar, tapioca, and cinnamon. Add the blackberries and apple slices. Toss gently until coated. Let stand for 15 minutes.
Spoon the filling into the pastry-lined pie plate. Dot with butter. Trim pastry even with edge of the pie plate. Moisten the edge of the pastry with water.
Roll out the remaining pastry as before. Cut slits in the pastry to let steam escape. Place pastry on the filling. Trim the top crust to 1/2 inch beyond edge of pie plate. Fold top pastry and crimp edge. Cover edge of crust with foil to prevent over-browning.
Bake in a preheated 375-degree oven for 25 minutes. Remove the foil. Bake for another 20 to 25 minutes or until the crust is golden brown and the filling is bubbly. Cool on a wire rack.