Place the ice cubes, mint leaves, tequila and simple syrup in the blender or cocktail shaker.
Squeeze in the juice from limes and divide the limes between each glass.
Blend or shake until well combined.
Divide between the glasses and top with soda water and sprigs of mint.
To make the simple syrup, place 1 cup of sugar and 1 cup of water in a saucepan and bring it to boil. Reduce the heat to a simmer and simmer until the sugar is dissolved. Rim ice from the heat and let cool completely before decanting into a sterilized bottle. Refrigerate for up to 1 month.