Add the tomatoes, water, vinegar, sugar and salt to the pitcher of a blender. Blend on high for 2 minutes. Pour into an 8-by-8-inch baking dish. Discard the seeds and any solids. Freeze for 2 hours.
After two hours, use a fork to scrape and break up the mixture. Stir to distribute the ice crystals and return to the freezer until frozen solid, about 2 hours more.
Use a fork to scrape the desired amount of large shards of ice into small bowls. Top each serving with basil, mozzarella quarters and pine nuts. Drizzle with olive oil and sprinkle with flaky sea salt and serve.
The granita can be made in advance and stored covered with plastic wrap for up to 4 days.