1Line shallow dish with parchment paper. In 2-quart saucepan, beat sugar and water with whisk until blended. Heat to boiling. Reduce heat to medium-low; simmer until mixture becomes a thin syrup. Cool.
2Remove most of peel from cucumbers. With spoon, scoop out seeds. Chop cucumber into cubes.
3In blender, place cucumbers, lime juice and syrup. Cover; blend until smooth. Pour into dish. Cover; freeze 2 to 3 hours or until completely frozen.
4Rake fork through mixture. Serve immediately, or return granita to freezer until ready to serve.