To prepare sorbet, bring 1/2 cup clementine juice to a boil in a small saucepan. Reduce heat; simmer until reduced to 1/4 cup (about 12 minutes).
Place chocolate in a large bowl. Combine 2 1/2 cups water and 3/4 cup sugar in a small saucepan; bring to a boil. Cook 1 minute; remove from heat. Pour over chocolate; let stand 2 minutes. Stir gently with a whisk until smooth. Add reduced clementine juice, 1/2 cup lemon juice, and vanilla to chocolate mixture, stirring well. Cool completely.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 1 hour or until firm.
To prepare sauce, combine 1 tablespoon water and cornstarch in a small bowl, stirring well with a whisk. Combine 1/2 cup clementine juice, 1/4 cup water, 2 teaspoons sugar, and 1 teaspoon lemon juice in a small saucepan; bring to a simmer. Add the cornstarch mixture to the juice mixture, and bring to a boil. Cook 1 minute or until thickened, stirring constantly.
Remove from heat, and gently stir in clementine sections. Cover and let stand 2 minutes. Serve sauce warm with sorbet.