Preheat oven to 400 degrees. On a lightly floured work surface, roll out pastry to a 10-by-12-inch rectangle. With a sharp knife, trim edges and cut pastry into eight 3-by-5-inch pieces. Place pastry on a large baking sheet and refrigerate until firm, about 15 minutes.
Transfer sheet to oven and bake until pastry is puffed and golden brown, 12 to 15 minutes. Let cool, then split each pastry horizontally.
In a bowl, mash blackberries and sugar with a fork until juicy but still chunky. Spread mascarpone on pastry bottoms. Top with blackberry mixture and pastry tops.