Peel and core the pears. Cut the pears into 1-inch chunks and place them in a small pot. Add the sugar and water. Bring to a boil over medium-high heat. Reduce the heat and simmer, stirring occasionally, until the pears have softened, and the liquid has reduced to thin syrup, for about 20 minutes. Remove from the heat and let it cool.
In a blender or food processor, combine the pears (with syrup), sake, mirin and ume vinegar. Blend into a smooth pure.
Pour the mixture into a shallow freezer-safe container. Freeze for about an hour, then, using a fork, scrape and stir to break up ice crystals. Return granita to freezer until firm, 8 to 12 hours, occasionally scraping and stirring with a fork.
To serve, remove the granita from the freezer and process in food processor. Spoon granita into small glasses or bowls and serve.