Preheat oven to 400 degrees F (200 degrees C). Grease 20 muffin cups.
Cut a 1/2-inch hole into the larger part of the squash and cover with a damp paper towel.
Cook squash in a microwave oven in 3-minute increments, turning slightly after each increment, until squash can be easily pierced with a fork, 9 to 12 minutes. Set aside until cool to the touch, about 20 minutes.
Halve squash lengthwise and scoop out seeds. Measure 1 1/2 cups squash into a large bowl. Mash eggs, water, vegetable oil, white sugar, and brown sugar into the squash. Whisk whole wheat flour, all-purpose flour, baking powder, baking soda, cinnamon, salt, nutmeg, cloves, and pumpkin pie spice into the squash mixture until you have a smooth batter. Fold raisins and walnuts into the batter.
Spoon batter into prepared muffin cups to about 1/2 to 2/3 full.
Bake in the preheated oven until a toothpick inserted into the center of a muffin comes out clean, about 15 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.