Combine 1 1/2 cups water and sugar in a small saucepan, and bring to a boil. Cook over medium-high heat for 2 minutes or until sugar dissolves, stirring constantly. Remove from heat; cool. Pour into a blender. Add blackberries and remaining ingredients; process until smooth. Strain mixture through a fine sieve into a bowl, and discard solids. Pour mixture into an 11 x 7-inch baking dish; cover and freeze 45 minutes. Stir blackberry mixture with a fork every 45 minutes until completely frozen and slushy (about 3 hours).
Remove blackberry mixture from freezer; scrape with a fork until fluffy.