Add the mint and sugar to a mason jar or sturdy glass. Use a muddler to pound the mint and release the oils. Cut the grapefruit in half crosswise and squeeze to get all of the juices in a bowl. Add the ice cubes to the jar and pour in grapefruit juice and rum. Close the lid and shake or stir vigorously until the sugar at the bottom has dissolved. Pour into a collins glass and garnish with quartered and sliced grapefruit.