1. Remove rind and white part from watermelon and discard. Cut pulp into 1 1/2-inch chunks (about 4-1/2 cups total); place in large bowl. Add superfine sugar and bottled sweetened lime juice; toss to combine. Refrigerate 30 minutes to 1 hour.
2. Transfer mixture to blender along with vodka. Blend until pureed. Serve immediately or refrigerate until serving. Garnish with thin slices of watermelon. Pour the martini.