Combine graham cracker crumbs, melted butter, and granulated sugar in a medium bowl. Stir until crumbs are evenly moistened.
Press mixture firmly onto the bottom and up the sides of a 9-inch springform pan.
In a large bowl, beat softened cream cheese until smooth. Gradually mix in sweetened condensed milk.
Stir in lemon juice and vanilla extract until fully incorporated.
Pour half the cream cheese mixture into the chilled crust. Spread it evenly.
Top with raspberry puree, leaving a slight border. Use a knife to gently swirl the puree into the cream cheese layer.
Spread the remaining cream cheese layer to cover entirely. Refrigerate for at least 4 hours to set.
Garnish with fresh raspberries before serving.