Preheat oven to 450 degrees. In a food processor, pulse flour, baking powder, baking soda, and salt. Add cheddar and sage and pulse to combine. Add butter and pulse until mixture is the texture of coarse meal, with a few pea-size pieces butter remaining. Add buttermilk and pulse just until combined, 2 to 3 times.
Turn dough out onto a lightly floured work surface and knead just until it comes together. With a floured rolling pin, roll dough to a 3/4-inch thickness. With a floured 2 3/4-inch round biscuit cutter, cut out 12 biscuits (reroll and cut scraps).
Place biscuits on a baking sheet, 1 1/2 inches apart, and bake until puffed and golden, 12 to 15 minutes. Transfer to a wire rack. Serve warm or at room temperature.