Preheat oven to 350 degrees F (175 degrees C). Line 2 muffin tins with cupcake liners.
Stir soy milk and apple cider vinegar together in a large bowl. Let stand until curdled, about 5 minutes. Mix in applesauce, oil, beet juice, and vanilla extract.
Combine flour, sugar, cocoa powder, baking powder, baking soda, and salt in a large bowl. Whisk to remove lumps. Pour in soy milk mixture; stir until batter is just combined.
Fill each cupcake liner 3/4 full with batter.
Bake in the preheated oven until the top springs back to the touch and a toothpick inserted into the center comes out clean, about 20 minutes. Cool for 5 minutes. Remove from the tins and place on wire racks until completely cool.