Combine 3 cups mint sprigs, sugar, and water in a large Dutch oven, stirring well. Bring to a boil. Reduce heat; simmer, uncovered, 10 minutes. Cool. Cover and refrigerate overnight.
Before serving, strain mint mixture; discard mint. Combine mint liquid, pineapple juice, lemon rind, and juice in a large punch bowl. Slowly pour ginger ale and tonic water into punch. Garnish with additional mint sprigs.