Preheat an oven to 425 degrees F (220 degrees C). Grease a 9x13-inch baking dish.
Place the blackberries into a large saucepan; add the cornstarch and 1 1/2 cup of sugar. Pour in the water, and bring to a boil over high heat, stirring constantly until the berries have thickened, about 5 minutes. Pour into the prepared baking dish.
Whisk the flour, baking powder, salt, and 2/3 cup of sugar together in a mixing bowl. Cut in the margarine until it is the size of peas. Stir in the milk until a soft dough forms, then drop by spoonfuls onto the hot blackberry topping.
Bake in the preheated oven until golden brown, 30 to 45 minutes.