Preheat the oven to 325°F. Line a mini muffin tin with paper liners.
In a mixing bowl, beat the softened cream cheese, granulated sugar, and vanilla extract until smooth and creamy. Add the egg and sour cream, mixing until fully combined.
In a separate bowl, combine the mixed berries, lemon juice, cornstarch, and cinnamon. Mash the berries slightly with a fork to create a chunky sauce.
Spoon about 1 tablespoon of the cheesecake mixture into each muffin cup. Add a teaspoon of the berry mixture on top of the cheesecake layer, then use a toothpick or skewer to swirl the berry mixture into the cheesecake.
In a small bowl, mix the graham cracker crumbs with melted butter. Sprinkle a small amount of the crumb mixture on top of each cheesecake bite.
Bake in the preheated oven for 15-18 minutes, or until the edges are set but the centers are still slightly jiggly. Remove from the oven and let cool to room temperature, then refrigerate for at least 2 hours before serving.