Bring water to a boil in a small saucepan. Stir in sugar until it dissolves into a syrup. Remove from heat; let cool completely, about 15 minutes.
Pour lychees into a blender; puree until smooth.
Combine 1/4 cup lychee puree and blueberries in a cocktail shaker; mash with a cocktail muddler. Add 1/4 cup syrup, ice, blueberry vodka, and sweet and sour mix. Cover and shake until the outside of the shaker has frosted. Strain into two cocktail glasses.
