Combine sugar and vinegar in a small, heavy saucepan. Bring to a boil; cook 6 minutes or until amber brown. Remove from heat; stir in liqueur.
Place the clementine sections in a large bowl; pour sugar mixture over sections. Cover and chill 2 hours, stirring occasionally. Combine milk and yogurt, stirring with a whisk. Spoon clementine mixture into individual bowls or stemmed glasses, and top with the yogurt mixture. Garnish with mint, if desired.