Cut off and discard peel and outer white membrane from 4 Mexican limes or 1 regular (keep peel on the rest). Quarter all limes, cut out and discard white cores, and seed.
Put 3 cups ice cubes in a blender, followed by the limes, frozen lemonade concentrate, simple syrup, mint leaves, chile, and sea salt. Whirl until very smooth, stirring often. Pour into glasses and add a mint sprig to each. Serve immediately.