Using a fine mesh strainer, place half of the watermelon chunks in the stainer over your first mug and carefully but firmly mash with the back of a spoon or other firm utensil, pushing the juice into the mug, but not the flesh of the watermelon. (Alternately, you can puree the watermelon in a blender of food processor and the strain into the mugs.) Repeat process with the remaining watermelon into the second mug.
Add half of the mint to each of the mugs (you can muddle the mint leaves if you like, or just leave them loose in there.)
Add 1 tablespoon of lime juice and 2 ounces of vodka to each mug, and then fill mugs half-way with ice.
Fill mugs with ginger beer (about 1/2 cup, but may be more or less depending on the size of your mug.)
Garnish with watermelon and mint on mini skewers, a cute straw, and enjoy!