Preheat oven to 350°F Line 12-cup muffin pan with paper liners.
In a small bowl, whisk flour, cocoa powder, baking soda, and salt.
In a large bowl, with electric mixer on medium speed, beat sugar, mayonnaise, and vanilla extract until combined. Beat in flour mixture in thirds, alternating with water, until blended. Beat 1 minute, scraping bowl occasionally. Divide batter evenly among muffin cups.
Bake 22 to 24 minutes, or until a toothpick inserted in cupcakes comes out clean. Let cool in pan 5 minutes before removing to wire rack to cool completely. Top with frosting.