For the cherry sauce: place cherries, water and sugar in a small saucepan and bring to a simmer over medium heat. Cook for about 10 minutes, stirring and smashing often, until cherries have broken down. Place in blender and carefully blend until completely smooth. Place in a jar and refrigerate until cold.
Cut each lime in half and squeeze 1/2 lime into each copper mug. Spoon 2 ounces (4 tablespoons) of the cherry sauce into each mug then 2 ounces of vodka into each. Stir until combined. Add crushed ice then 1/2 cup ginger beer into each. Stir lightly to combine. Garnish with limes slices and cherries.