Lay out in a single layer on a parchment paper covered baking sheet.
Cover with plastic wrap and freeze for at least 2 hours.
Cut 3 or 4 slices from the other half of the watermelon. Then cut them into 6 or 8 pieces each. These will be soaked in the alcohol.
With the remaining watermelon, cut smaller wedges to be used for garnish on the glasses. Cut a small slit in the side of each one. Wrap in plastic wrap and refrigerate until serving.
Combine 2 bottles of rosé wine, ½ cup watermelon liqueur and ¼ cup lime juice in a large pitcher or drink dispenser.
Cover and refrigerate for at least 2 hours or overnight.
When you're ready to serve, pour the bottle of club soda into the alcohol mixture.
To fill each glass, add a few ice cubes and frozen watermelon cubes. Then pour in the sangria.
To garnish, push a slice of lime down the side of the glass, put a small watermelon slice on the edge of the glass, and top with a sprig of mint.
Notes
For a stronger drink, add an additional ½ cup watermelon liqueur or rum.
For a sweeter cocktail, use 7-Up or Sprite instead of club soda.
To prevent the drink from getting watered down, put ice cubes in each individual glass rather than the pitcher (or drink dispenser).