Scoop cantaloupe meat into a bowl and mash with a potato masher until smooth. Run cantaloupe through a strainer, collecting juice in a measuring cup. Collect 1 1/2 cup cantaloupe juice, adding enough mango juice to reach 1 1/2 cups as needed. Discard cantaloupe pulp or reserve for another use.
Pour juice mixture into a bowl; mix in water and sugar until sugar is dissolved.
Transfer juice mixture to an ice cream maker and follow manufacturer's instructions for sorbet.