In small bowl, soak raisins or currants in enough warm water to cover, until soft, about 10 minutes. Drain.
In small skillet over medium-high heat, toast pine nuts, shaking pan often until lightly browned, 1 to 2 minutes.
Peel mango and cut small slice off one end. Place mango, cut side down, on cutting board and work around pit, cutting each side of mango into large slices. Use paring knife to cut flesh away from pit. Roughly chop fruit into small pieces.
In medium bowl, combine mango with pine nuts, remaining ingredients and salt to taste; mix well. Cover and refrigerate for at least 30 minutes before serving. Chutney will keep in the refrigerator for up to 2 days.