In a small pitcher combine sliced cucumber from half the cucumber, tequila, grapefruit juice, lime juice, triple sec, and simple syrup. Stir and chill until ready to serve.
Before serving, rub lime across the rim of four tall glasses. Dip the rim of each glass in salt. Fill each glass with crushed or small cubes of ice. Add lime rounds, remaining cucumber slices, and a wedge of grapefruit.
Fill each glass with chilled margarita and enjoy immediately.
