Have ready a high ball glass.
Press mint leaves between hands with a clap, this releases the aroma. Place mint leaves, the mandarin quarters, juice and sugar into the high ball glass. Using a muddler or rolling pin gently press to crush mandarin pieces with the sugar. The crushing action releases the mandarin juices and essential oils from the skin. Add the rum and enough crushed ice to half fill glass. Stir to combine and dissolve sugar. Add more crushed ice to fill glass. Top with soda water. Place mint sprig to garnish.