Combine rosemary, sugar and water for the simple syrup in a small saucepan. Bring the mixture to a boil over medium-high heat and cook until the sugar is dissolved completely. Remove from heat and allow to steep for 30 minutes. Remove rosemary sprigs and store the simple syrup in an airtight container in the refrigerator.
To create the cocktail, add the syrup and mint leaves to a shaker. Muddle.
Fill the shaker with ice and add the whiskey, lemon juice, and pineapple juice. Shake for 10 to 15 seconds. Strain into a rocks glass filled with crushed ice. Garnish with a rosemary sprig and serve.