Using a blender or food processor, puree mint and sake for 2 minutes. Strain through a fine chinois into a bowl, removing any solids. Mix in lime juice and 8 ounces of pineapple juice. Wrap with plastic wrap and refrigerate until chilled.
Pour 8 ounces of pineapple juice into a resealable plastic bag. Place in freezer on a flat surface for one hour or until frozen. Using a blender, puree frozen pineapple juice and sake mixture until fully combined, about 1 minute.
Pour 3/4 cup of mixture into each of 5 glasses. Let rest 1 minute for mixture to separate and top with pineapple slices.