Combine wine or juice, water, and sugar in a medium saucepan. Bring to boiling, stirring occasionally, until sugar is dissolved. Add cranberries, grapes, grated ginger, if using, and cloves; return to boiling. Reduce heat and cook, covered, for 15 minutes, stirring occasionally. Uncover and cook 10 minutes more, stirring occasionally.
To serve, stir in mint, if using. Serve warm or chilled. Makes 6 (1/4-cup) servings.