The NY Times has an article on making sorbet or granita. Sorbets need 
some corn syrup or honey to prevent ice crystals from forming, but 
granitas, by definition, have ice crystals. See:

http://well.blogs.nytimes.com/2012/07/13/sorbets-of-summer/

One of the five recipes is for watermelon sorbet or granita. It would 
seem to be the one that could be made with no sweetener added at all. 
Below is the recipe edited to only be for granita. Maybe someone 
could try it and post their results here. (Some of the container 
instructions are a bit strange, but that is the way they are.)

Watermelon Granita
------------------
This works only if your watermelon is juicy and sweet.

2 pounds watermelon, seedless if possible, or seeded if seedless is 
not available, cut into 1-inch chunks

2 tablespoons fresh lime juice

Pinch of salt

1. Place the ingredients in a blender, and blend until smooth. Chill 
in the refrigerator for 2 hours or overnight.

2. Place a 9-by-11-inch baking dish in the freezer.

3. Place a container in the freezer. Using an immersion blender, 
blend the watermelon mixture for 30 seconds. Scrape into the chilled 
baking dish and place back in the freezer. Set the timer for 30 
minutes. Using a fork, scrape the ice crystals from the outside of 
the baking dish toward the center. Return to the freezer and set the 
timer for another 30 minutes. Continue to scrape the mixture with a 
fork every 30 minutes until you have a uniform frozen mixture. It 
should not be frozen solid. If you forget to scrape and the mixture 
does freeze like an ice cube, cut into chunks and use a food 
processor fitted with the steel blade to break it up. Transfer to a 
container and freeze. Allow to soften for 15 minutes in the 
refrigerator before serving.