Preheat the oven to 325 degrees Fahrenheit (163 degrees Celsius) and grease a 9-inch springform pan.
Combine graham cracker crumbs, 0.25 cup sugar, and melted butter in a bowl; press firmly into the bottom and 1 inch up the sides of the pan.
Bake the crust for 10 minutes, then remove from the oven and set aside to cool.
In a large mixing bowl, beat the cream cheese and remaining 1 cup sugar until smooth and aerated.
Mix in the sweet potato puree, sour cream, vanilla extract, cinnamon, ginger, nutmeg, and salt until fully incorporated.
Add eggs one at a time, beating on low speed after each addition just until combined to avoid over-incorporating air.
Pour the batter over the prepared crust and smooth the top with a spatula.
Bake for 65 to 75 minutes, or until the edges are set and the center slightly jiggles when the pan is moved.
Turn off the oven and crack the door open, allowing the cheesecake to cool inside for 1 hour to prevent cracking.
Remove from the oven and cool completely at room temperature, then refrigerate for at least 6 hours or overnight before serving.