Preheat the oven to 400 degrees. Prepare a baking sheet with a silicone mat or line the baking sheet with parchment paper.
In a medium sized mixing bowl, combine the flour, sugars, baking powder, baking soda, and salt. Add the butter and cream cheese. Using a fork, a pastry blender, or your fingers, cut in the butter and cream cheese until the mixture is coarse with no lumps larger than pea-sized. Gently stir in the blackberries. Add the buttermilk and vanilla and stir until just combined.
Turn the scone dough out onto a lightly floured surface and using floured hands, lightly knead the dough 3 or 4 times. Shape the dough into an 8 inch round with a thickness of about 1 inch.
Place the dough onto the prepared baking sheet and cut into 8 wedges, separating them slightly.
Bake for 20-25 minutes or until golden brown. Remove to a wire rack to cool.