Combine first 5 ingredients in a small saucepan over medium heat; bring to a boil. Cook 1 minute; remove from heat. Add mint; let stand 10 minutes. Discard mint. Place juice mixture and cucumber in a blender; process until smooth. Cool completely. Pour mixture into an 11 x 7inch baking dish. Cover and freeze for 45 minutes; scrape with a fork. Freeze. Scrape mixture every 45 minutes until completely frozen (about 3 hours). Remove from freezer; scrape with a fork until fluffy.