Place first 6 ingredients in a blender; process until smooth. Cover and chill.
Cut the cucumber lengthwise into 4 pieces; cut each piece crosswise into 6 (1/4-inch) slices. Bring water to a boil in a medium saucepan. Add chicken; cook 4 minutes or until done. Drain well, and cool. Thread 1 chicken piece, 1 cucumber piece, and 1 mint leaf onto each of 24 (6-inch) skewers. Cover and chill. Serve with sauce; garnish with cucumber slices, if desired.