Combine gingersnaps and butter; stir well. Press mixture into a 9-inch round removable-bottom tart pan coated with cooking spray. Bake at 350° for 9 minutes or until lightly browned. Cool on a wire rack.
Place peaches and 1/3 cup sugar in a blender; process until smooth. Combine gelatin and boiling water; stir until gelatin dissolves. Add gelatin mixture to blender; process 15 seconds. Transfer peach mixture to a large bowl; cover and chill 1 hour.
Combine raspberries and next 3 ingredients in a small saucepan; bring to a boil. Reduce heat, and simmer 5 minutes or until mixture thickens. Strain mixture through a sieve into a bowl; discard solids. Cover and chill 30 minutes.
Fold whipped topping into peach mixture. Pour onto prepared crust. Spoon raspberry mixture over peach mixture; swirl mixtures together using a knife. Cover and chill 8 hours. Remove sides of pan before serving.