In a large bowl, combine the first six ingredients; beat on low speed for 30 seconds. Beat on medium for 2 minutes. Fill paper-lined muffin cups half full. Place one clementine section in the center of each; gently press down into batter. Chop remaining sections; sprinkle over batter.
Bake at 350° for 15-20 minutes or until a toothpick inserted in the center comes out clean. Cool for 10 minutes before removing from pans to wire racks to cool completely.
For frosting, in a small bowl, beat butter until light and fluffy. Beat in the confectioners' sugar, clementine peel and enough juice to achieve spreading consistency. Frost cupcakes.
In a small microwave-safe bowl, melt chocolate chips; stir until smooth. Dip clementine sections halfway into chocolate; allow excess to drip off. Place on a waxed paper-lined baking sheet; refrigerate until set. Place one on each cupcake.