Cut the watermelon into 1-inch chunks and remove any visible seeds.
Add watermelon chunks to a blender and blend until smooth, about 30 seconds.
Pour the watermelon puree through a fine mesh strainer into a bowl, pressing gently with a spoon to extract juice.
In a pitcher, muddle mint leaves gently to release their flavor.
Add the strained watermelon juice, lime juice, and honey to the pitcher. Stir until honey dissolves completely.
Refrigerate mixture for at least 30 minutes to chill thoroughly.
When ready to serve, fill glasses halfway with ice cubes.
Pour the watermelon-lime mixture into each glass, filling about 3/4 full.
Top each glass with sparkling water and stir gently to combine.
Garnish with mint leaves, lime slices, and small watermelon wedges.