Combine mint, sake, and sugar in a blender; process for 2 minutes or until mint is very finely chopped. Strain sake mixture through a fine sieve over a bowl; discard solids. Stir in 2 cans pineapple juice and lime juice. Cover and chill.
Pour the remaining 1 can pineapple juice into a zip-top plastic bag; seal. Lay the bag flat in the freezer; freeze 1 hour or until frozen. Combine the sake mixture and frozen pineapple juice in a blender; process 1 minute or until thoroughly combined. Pour about 3/4 cup pineapple mixture into each of 5 glasses, and let stand 1 minute before serving. Garnish with pineapple slices, if desired.