In a medium bowl, mix 3/4 cup of sugar into the cream cheese. Mix in the eggs one at a time, then stir in the vanilla. Pour this batter into the graham cracker crust, and smooth over the top.
Bake in preheated oven until the edges have puffed up but the middle still jiggles, about 30 minutes. Allow to cool for 30 minutes, then refrigerate until cold, about 3 hours.
While the cheesecake is baking, pour 1 cup of the mango nectar and 1/3 cup of sugar into a saucepan, and bring to a boil over medium-high heat, dissolving the sugar. Dissolve the cornstarch in the remaining 1/4 cup of nectar, and stir into the boiling saucepan until thickened and clear, about 30 seconds. Place diced mango into a heatproof bowl, and toss with the thickened sauce. Allow to cool to room temperature, then pour over the cheesecake. Serve cold.