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.
To make watermelon ice cubes for serving, pour extra watermelon juice into ice cube trays and freeze overnight.