Add some watermelon chunks to a blender (I used about 2-3 cups because I like to keep some leftover juice in the fridge). Blend well until watermelon is pureed. Strain over fine mesh strainer into container. Save juice, discard pulp.
To make a Watermelon Moscow Mule:
Combine watermelon juice, vodka, ginger liqueur and lime juice in cocktail shaker filled with ice. Shake well, Strain into tall glass filled with ice. Top with ginger beer.
*or try just muddling a few chunks of watermelon in bottom of glass if you prefer not to make watermelon juice.