Squeeze the whole lime to get 2 tablespoons juice. Cut a slice from lime half for a garnish and set aside.
Run remaining piece of lime around rim of a 6-ounce cocktail glass. Dip moistened rim in a plate of salt (as you would rim a margarita glass). Chill glass until ready to use.
Fill cocktail shaker with ice and add tequila, Tuaca liqueur, cranberry juice, and 2 tablespoons lime- juice. Shake vigorously to chill, strain mixture into the chilled glass. Garnish with the lime slice.