1. In a saucepan, combine the sugar and water. Bring to a simmer over moderate heat, stirring until the sugar dissolves. Remove from the heat and let cool.
2. In a blender, combine half of the sugar syrup with half of the lime juice, rum, and watermelon chunks and blend until combined. Add half of the ice and blend until smooth, then pour into a large pitcher.
3. Repeat with the remaining ingredients. Serve in chilled glasses, garnished with watermelon spears and topped with mint sprigs.

Makes 2 1/2 quarts.

Make ahead: the watermelon mixture can be blended earlier in the day and refrigerated. Blend with ice just before serving.