Carefully peel the kiwi whole, slice one middle section slice for garnish, and dice up the rest of the kiwi into small pieces. With a fork, mash up the kiwi pieces on the cutting board as well as you can. Alternatively, you can use a muddler inside the cocktail shaker if you have one.
Fill a cocktail shaker with ice. Place the mashed kiwi inside the cocktail shaker. Add the tequila, Cointreau (or Triple Sec), lime juice, and simple syrup if using. Shake well until the sides are frosty.
Serve:
To a glass filled with ice, strain the mixture through the strainer to remove kiwi seeds. If you enjoy fruity tidbits in your drink, skip this step.
Garnish with a kiwi slice and a mint sprig for added flavor. Enjoy!