Fill a copper mug or a highball glass to the top with crushed ice. Using crushed ice is traditional for mules as it keeps the drink colder and provides a better texture for sipping.
Pour the cranberry juice and the freshly squeezed lime juice over the ice. Using unsweetened cranberry juice allows you to enjoy the natural tartness, while the lime adds a bright, zesty note.
Slowly pour the chilled ginger beer into the mug until it reaches the top. The carbonation will naturally mix with the juices, but you can give it a very gentle stir with a long spoon to ensure the flavors are combined without losing the bubbles.
Drop a few fresh cranberries on top of the ice. Add a sprig of fresh rosemary for a woody aroma or a lime wedge for extra acidity. Serve immediately while the drink is fizzy and cold.