From http://www.foodandwine.com/recipes/watermelon-tequila-cocktails

2 oz silver tequila
1/2 oz fresh lime juice
1/4 oz simple syrup

2 cups diced seedless watermelon (1 pound)
~5 blueberries
1/4 cup loosely packed chopped fresh mint leaves, plus some garnish

In a blender, puree the watermelon until smooth. Set a fine-mesh strainer over a bowl and strain the watermelon juice, pressing gently on the solids to extract as much juice as possible. Discard the pulp.

4.0 parts White Rum or Cachaca (cut down the sugar if using cachaca)
3.0 parts lime juice
3 sprigs of Mint
2 teaspoons Sugar
Soda Water (or just water)

In an old fashioned glass, muddle most of the mint with sugar and slices of lime plus a dash of lime juice. Add in ice, Mix in rum and soda water. Garnish with sprig of mint.

2 oz bourbon
8 sprigs of mint
1 tsp of sugar

Muddle mint and sugar in mixing glass. Add shaved ice and bourbon. Shake until frosted and pour all into rocks glass full of crushed or shaved ice. Garnish with a mint sprig.

See also:
http://usumcasane.tumblr.com/post/555114642 for crushed-mint-in-the-glass style
and
http://www.foodnetwork.com/recipes/sara-moulton/the-perfect-mint... for extracting mint beforehand.