Combine 1/2 cup grapefruit juice and honey in a small saucepan.
Cook over low heat until honey melts.
Place mint in a large bowl.
Pour honey mixture over mint; stir well.
Line a colander or sieve with a double layer of cheesecloth that has been rinsed our and squeezed dry.
Allow cheesecloth to extend over outside edges of colander.
Place colander in a large bowl to drain.
Pour honey-mint mixture into colander.
Transfer honey mixture to a small saucepan.
Sprinkle gelatin over honey mixture in saucepan; let stand 5 minutes.
Cook over low heat, stirring constantly, until gelatin dissolves.
Combine gelatin mixture, remaining 3 1/2 cups grape-fruit juice, and lemon juice in a large bowl; stir well.
Cover and freeze until firm.
Remove from freezer; let stand 10 minutes.
Position knife blade in food processor bowl; add frozen mixture.
Top with cover, and process until smooth.