In a blender or food processor, puree all ingredients until smooth. Using a fine mesh strainer, pour the puree into a loaf pan, pressing down on solids to get all the juice out. Place loaf pan, uncovered, in freezer for 30 minutes.
Remove from freezer. Use a fork to scrape at the frozen portions, breaking them up. Place back in freezer for 30 minutes, then repeat scraping. Continue for 2 to 4 hours, scraping and freezing, until mixture resembles shaved ice. Serve immediately with chopped blackberries for garnish.