Position knife blade in food processor bowl; drop cranberries through food chute with processor running, and process 15 seconds or until minced. Transfer cranberries to a small bowl.
Position knife blade in processor bowl; add kumquats, ginger, and pepper. Pulse 3 to 5 times or until mixture is finely chopped.
Add kumquat mixture to cranberries. Stir in sugar and mint. Cover and store in refrigerator. Flavor intensifies the longersalsa is chilled. Serve with chicken, pork, or turkey or as a spread over nonfat cream cheese; or stir into low-fat yogurt.