Preheat oven to 350 degrees F (175 degrees C). Grease and flour two 9x5-inch loaf pans.
Mix white sugar, pumpkin puree, vegetable oil, eggs, and water together in a large bowl until smooth. Whisk baking flour, baking mix, pumpkin pie spice, baking soda, and baking powder together in a separate bowl; stir into pumpkin mixture until batter is just blended. Pour batter into the prepared pans.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 50 minutes.
Beat cream cheese, confectioners' sugar, and milk together in a bowl using an electric mixer until icing is smooth. Spread icing over pumpkin bread.