Put the lime juice, sugar and mint spring in a pan. Warm over a low heat, stirring continuously, until the sugar has dissolved.
Remove from the heat and set aside to cool. Discard the mint. In a blender whizz the watermelon until the fruit has broken down.
Using a spatula, push the watermelon mixture through a fine sieve into a freezer-proof bowl. Discard the pips left in the sieve.
Add the pomergrante juice and the lime juice. Cover the bowl and freeze for 4-5 hours, raking with a fork every hour to break up and disperse the ice crystais. The mixture should resemble slushy ice.
To serve, spoon the mixture into glasses.