In a medium saucepan, combine 1 cup of water and the sugar. Heat over medium heat, stirring until the sugar is completely dissolved. Remove from heat and let it cool to room temperature.
In a blender, combine the fresh raspberries and the remaining 3 cups of water. Blend until smooth.
Strain the raspberry mixture through a fine mesh sieve into a large pitcher to remove the seeds.
Add the cooled sugar syrup, fresh lime juice, and vanilla extract to the pitcher. Stir well to combine.
Chill the mixture in the refrigerator for at least 1 hour before serving.
To serve, fill glasses with ice cubes and pour the tropical lime raspberry refresher over the ice. Garnish with fresh mint leaves if desired.