Place cranberries, sugar, and water in a small saucepan over medium-high heat. Bring to a boil, stirring occasionally, then reduce heat to medium and simmer 10 minutes or until cranberries begin to release their juices.
Remove from heat and transfer cranberries and juices to a food processor and blend several times until mixture is smooth. Strain cranberry mixture through a fine-mesh sieve, discarding solids.
In a cocktail shaker, combine strained cranberry puree, orange juice, and vodka. Add ice to shaker, screw lid on and shake several times until condensation begins to form on outside of shaker.
Divide shaken cranberry mixture between 3 glasses. Add ice, a few fresh cranberries, and orange wedges to each glass then top each drink with 4 oz chilled ginger beer. Serve moscow mules immediately and enjoy!