Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Combine flour, sugar, cinnamon, baking powder, salt, and cloves in a bowl and mix well. Add cooled coffee, oil, and sweet potato puree; mix well. Pour batter evenly into the prepared baking pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 25 to 30 minutes. Remove and allow to cool on a wire rack, about 30 minutes.
Stir together 1 cup confectioners' sugar, 1 tablespoon orange juice, vanilla extract, and cinnamon in a bowl. Add more sugar or orange juice, if needed, to achieve your desired consistency. Drizzle icing over the top of the cooled cake.