In a medium bowl, mix the beer, water, and sugar together, stirring until the sugar dissolves.
Pour the mixture into a shallow baking dish and put it into the freezer until partially frozen. Use a fork to scrape and break the mixture into shards and crystals. Return the pan to the freezer to freeze completely. Scrape and toss the granita one more time. Keep frozen until serving. Serve in stemmed glasses, dolloped with whipped cream, if desired.