Grate enough grapefruit rind to make 1/2 cup zest; set aside.
Juice grapefruit to make 2 cups juice.
Strain juice to remove any seeds, reserving pulp.
Add pulp to juice; set aside.
Place sugar, water and zest in 1 quart saucepan; stir well.
Bring to a boil over medium-high heat.
Remove from heat; remove 3/4 of zest with slotted spoon.
Place zest in airtight container and refrigerate until sorbet is ready to serve.
Let grapefruit syrup cool.
Combine cooled sugar mixture, reserved grapefruit juice and lime juice; cover and refrigerate until cold.
Place mixture in ice cream maker and freeze according to manufacturers directions.
Transfer sorbet to 1-quart plastic container.
Cover with plastic wrap and plastic lid to prevent ice crystals from forming.
Freeze until ready to serve.
Let stand 10 minutes to soften before serving.
Garnish each serving with reserved candied zest and mint leaves.