Add watermelon chunks, lemon juice, sugar, and 1/2 cup of the rosé to a food processor.
Cover and pulse a few times then add remaining rosé wine. This step prevents a lot of splatter that I find happens when I add all of the rosé at once.
Turn food processor on low for about 30 seconds or until mixture is smooth and free of any large watermelon chunks. Small watermelon chunks are ok.
Pour into a small, freezer-safe dish and freeze for at least two hours.
Scrape a spoon across the surface of the frozen mixture to get the little signature granita curls. Scoop them into a glass to serve and eat with a spoon.