Preheat oven to 325F.
Meanwhile, in a large mixing bowl, combine cream cheese, eggs, vanilla, 3/4 cup of sugar. Beat on low for 1-2 minutes. Remove 1 1/2 cups of the batter, put it into a separate bowl and set aside.
Add pumpkin puree, remaining 1/4 cup of sugar, cinnamon, nutmeg, and cloves to the remaining cheesecake batter.
Pour the pumpkin cheesecake batter into the cooled gingersnap crust. Spoon some of the white cheesecake batter onto 6 sections of the pumpkin cheesecake. Make swirls: Dip a knife in a straight horizontal line from one side of the cake to the other four times about 2 inches apart. Repeat from top to bottom.
Bake the swirled cheesecake on 325F for about 55-60 min. on the middle rack position in the oven. Place a pan of water on the rack underneath the cake to help avoid cracking. Let the cake cool for 40 minutes or longer before moving to the refrigerator to get cold.
Drizzle 1-2 tablespoons of caramel ice cream sauce on top of the Pumpkin Swirl Cheesecake before serving.