Puree the watermelon in a blender, and then strain the juice through a fine sieve or cheesecloth. Alternatively, use a juicer, or push the fruit through a fine sieve into a large bowl to collect the juice and eliminate the pulp and seeds. You can strain a second time with an even finer sieve or cheesecloth to remove the fine particles of pulp. Set aside.
Mix the salt and lime juice in a large pitcher. Stir in the watermelon juice, liqueur and vodka, and then taste and adjust the seasonings, if necessary. Stir well once more just before serving over ice.
Cook's Note: To make watermelon ice cubes for serving, pour extra watermelon juice into ice cube trays and freeze overnight.