Heat oven to 350°F. Place paper baking cup in each of 24 regular-size muffin cups. In large bowl, beat cake mix, water, oil and eggs with electric mixer on low speed 30 seconds; beat on medium speed 2 minutes, scraping bowl occasionally. Stir in baking chips. Divide batter evenly among muffin cups, filling each 3/4 full.
Bake 21 to 26 minutes or until toothpick inserted in center of cupcake comes out clean. Cool in pan 10 minutes. Remove cupcakes from pan; cool completely, about 45 minutes.
Stir peppermint extract into frosting until well blended; spread on cupcakes. To garnish each cupcake, cut 1 gumdrop into 4 slices. Place 3 rounds on cupcake to make shamrock leaves; press remaining round into thin strip and place below leaves for stem.