Preheat oven to 325 degrees. Lightly grease a 9-inch springform pan with vegetable oil.
Prepare the crust. In a food processor, process coconut, almonds, sugar, and salt until mixture resembles a coarse meal. Add melted butter and process until fully combined. Pour crust mixture into prepared pan and press crumbs evenly on the bottom and 1/2 inch up the sides. Bake until lightly browned, about 10 to 12 minutes. Remove from oven and set aside.
Prepare the filling. In a food processor, process cream cheese until smooth. Add mango and process again until smooth. Add sugar, salt, eggs, lemon juice, and potato starch. Process all ingredients until creamy and smooth.
Pour filling over baked crust. Place pan on a baking sheet and bake at 325 degrees until center is just set but still slightly jiggly, about 40 to 45 minutes. Cool to room temperature on a wire rack, about 1 1/2 hours.
Prepare the topping. In a medium saucepan, combine mango, apricot preserves, water, lime juice, and potato starch. Mix together and cook over medium heat until thickened and mango chunks are soft. If mixture gets too thick and starts to stick to the pan, add more water 1 tablespoon at a time. Remove from heat and puree in a food processor until smooth, or use animmersion blender.
Spoon mango mixture on top of cooled cheesecake and smooth the surface.
If desired, toast coconut in a small skillet over medium heat until it just begins to brown, about 3 to 4 minutes. Remove from heat and sprinkle over the mango topping.
Cover pan and refrigerate until chilled, at least 6 hours and up to overnight.
To serve, cut into wedges and garnish with fresh mango slices, if desired.