1. Cut and core pineapple into chunks. Mix pineapple pieces with ½ cup of sugar, and refrigerate for a minimum of 1 hour (3 hours is preferable).
2. In a medium saucepan, bring water and corn syrup to a slow boil. Add remaining ¼ cup of sugar, and the mint leaves. Stir while sugar dissolves, then turn off light, cover, and let the syrup mixture sit on stove for 1 hour. After one hour, pour mixture through a sieve to remove mint leaves, and chill syrup in refrigerator for the remaining 2 hours.
3. Remove pineapple and pulse in blender until smooth (can be left somewhat chunky, if this is your preference). Mix pureed pineapple and syrup together to combine well, then mix in ice cream maker according to manufacturers instructions.
4. Chill in freezer for 4 hours, or overnight.