Combine water, honey, chili and salt in a pan and bring to a boil. Remove pan from heat; cover and let stand 20 minutes. Remove and discard chili.
Transfer mixture to a blender. Add mango and both juices; process until smooth. Pour into a 2-quart electric ice cream maker and freeze according to manufacturer's instructions. Transfer sorbet to a freezer-safe container; cover and freeze until firm, about 2 hours.