Puree the cubed watermelon pulp in a food processor or blender until smooth.

Transfer the watermelon puree to a bowl.

In a stainless steel or enameled saucepan, combine the sugar, lime juice, lime rind, and water.

Bring the mixture to a boil, stirring to dissolve the sugar.

Simmer the syrup for 5 minutes, then let it cool completely.

Stir the cooled syrup into the watermelon puree.

Pour the mixture into an 8-inch square baking dish.

Freeze the mixture until firm, but not completely frozen.

In a chilled bowl, beat the partially frozen mixture until smooth.

Return the smoothed mixture to the baking dish.

Freeze for 3 hours or until solid.

Let the granita stand at room temperature for a few minutes until it is soft enough to scoop.