Begin by zesting the limes. Pour the coarse sugar over the lime zest and toss with your fingers to combine. Set aside.
Throw the mango into the blender. Top off the blender with ice. Pour the tequila and triple sec. Add the granulated sugar and squeeze in the juice of the limes. Blend until completely smooth, adding more ice if necessary to get it the consistency you want.
Use a piece of one of the limes to moisten the rim of the glasses. Dip the rims of the glasses in the lime sugar.
Pour the drinks and serve them immediately.