Put the mint, lime juice and Simple Syrup in a pitcher. Muddle for a few seconds to release the flavor from the mint.
Pour in the coconut water and rum. Add ice to fill a pitcher, and stir to combine and chill.
Stir together the sugar and 1 cup water in a medium pot. Bring to a simmer over medium-high heat. Stir to make sure all the sugar is dissolved. Simmer for 1 minute, and then remove from the heat. Cool completely.