In a food processor blend together the chopped mango, water, apple juice, lime juice and half of the lime zest (reserve the rest for garnish) until smooth. Taste the mixture - if it isn't sweet enough add the agave and blend again until combined.
Pour the mixture into an empty ice cube tray and freeze until solid (at least 5-6 hours).
When you're ready to make the cocktails - place the frozen mango purée cubes into a blender with the rum and blitz until smooth and creamy. Pour into two glasses and serve (garnished with the reserved lime zest, if you want).