Spray a 9-by-9-inch straight-sided cake pan with cooking spray, and then line with 2 pieces of parchment paper that overlap each other, leaving at least 1-inch of overhang on each side of the pan.
Add the graham crackers, almonds, brown sugar and salt to a large plastic resealable bag. Seal the bag, and then use a rolling pin to crush into fine crumbs. Add the butter, close the bag again and use your hands to thoroughly mix the butter into the crumbs. Press the crumbs into the bottom of the prepared pan and use a metal spatula to press the crust firmly into the corners. Place in the freezer while you prepare the filling.
Whip the heavy cream in a large bowl with an electric hand mixer until stiff peaks form. Combine the cream cheese, yogurt and confectioners' sugar in a medium bowl. Beat with the hand mixer until the mixture is completely smooth, light and fluffy. Fold the whipped cream in thirds into the cream cheese mixture, folding until just combined.
Spoon the cream cheese mixture onto the graham cracker crust and use an offset spatula to smooth out the top. Sprinkle evenly with the mango pieces, and then use your hands to gently press the mango into the top of the cheesecake. Put in the freezer for 1 hour to set.
Use the parchment paper to carefully lift the cheesecake out of the pan and transfer to a cutting board. Cut into 9 to 12 pieces and serve immediately.