Preheat oven to 400 degrees F (200 degrees C). Grease a 24-cup mini muffin tin with cooking spray.
Stir water and flaxseed meal together in a small bowl. Let stand until thickened, about 5 minutes.
Combine tapioca flour, potato starch, and baking powder in the bowl of a food processor; blend until well combined. Add vegan Mozzarella cheese; mix well. Mix in flaxseed mixture, almond milk, and olive oil, with the processor running, and blend until a smooth and soft batter forms.
Spoon batter into the prepared mini muffin tin, filling each 2/3 to the top.
Bake in the preheated oven until cheese breads are puffy and lightly golden, about 20 minutes.