In a food processor, pulse the strawberries and sugar until smooth.
Fill a cocktail shaker halfway with ice; add the tequila, triple sec, lime juice and 2 1/4 oz. strawberry puree. (Leftover puree will keep, refrigerated, up to 3 days.) Cover; shake vigorously until cold, about 15 seconds. Strain into a glass. Garnish with the strawberry.