In a large saucepan or Dutch oven, combine the sugar, apple cider vinegar, water (or orange juice), cinnamon, ginger, cloves, and salt.
Bring the mixture to a boil over medium-high heat, stirring occasionally until the sugar has completely dissolved.
Add the rinsed cranberries, diced apples, golden raisins, and dark raisins to the pot. Stir well to coat the fruit in the liquid.
Reduce the heat to low and simmer the mixture gently, uncovered. Stir occasionally to prevent sticking.
Cook for approximately 15 to 20 minutes, or until the cranberries have popped, the apples are tender, and the mixture has thickened to a jam-like consistency.
Remove the pot from the heat. Stir in the chopped pecans (or walnuts).
Allow the chutney to cool completely at room temperature. The texture will continue to thicken as it cools. Transfer to a serving dish or airtight container and refrigerate until ready to serve.