Preheat oven to 350° F. Wrap the outside of a 6-inch spring form pan with foil. Set aside.
Combine graham cracker crumbs, melted butter, and sugar in a medium bowl and mix to combine. Press the coarse, sandy mixture evenly over the bottom of the prepared springform pan. Pack the crust down with the bottom of a small measuring cup or glass. Bake until lightly toasted and firm, about 10 to 12 minutes. Leave the oven on and cool the crust on a rack while preparing the filling.
For the raspberry sauce, whisk together granulated sugar and cornstarch in a small sauce pan. Add cold water and raspberries. Warm over medium heat, whisking occasionally, until mixture comes to a boil. Simmer gently, whisking frequently until the sauce thickens, about 5 minutes. Strain the berry mixture over a fine mesh sieve into a small bowl, pressing with the side of a silicone spatula to separate the sauce from the seeds.
In the bowl of a standing electric mixer fitted with the paddle attachment, beat the cream cheese on medium until fluffy, about 5 minutes. With the mixer running, add sugar in a thin, steady stream, beating until smooth.
Reduce mixer speed to low and add eggs, one at a time, allowing each one to incorporate fully before continuing. Slowly pour in the cream and then add the vanilla. Mix until smooth, about 5 minutes.
In the meantime, bring a large kettle of water to boil and place a roasting pan in the oven. Check the that the foil on the spring form pan has no holes or gaps; if needed, add an extra layer of foil to prevent water from entering the pan during baking.
Pour about half of the filling into the spring form pan. Drizzle 3 tablespoons of the raspberry sauce over the filling, leaving a border of at least an inch around the sides of the pan. Swirl the sauce into the filling with a skewer or toothpick. Ladle remaining filling into the pan, starting around the edges first and ending in the center (this will keep the raspberry from showing through on the sides). Jiggle the pan or tap it on the counter gently to even out the top.
Fill the medicine dropper with raspberry sauce and add small dots of sauce over the top, spiraling out from the center. Starting in the center, pass the tip of a skewer or toothpick through the middle of each dot in a steady, continuous motion until you pass through the final circle. Save remaining raspberry sauce for serving.
Place the cheesecake in the roasting pan and pour boiling water in the roasting pan about 3/4 of the way up the sides of the spring form pan. Bake until the filling is set and just barely jiggles in the center, about 80 to 90 minutes. Remove cheesecake from the water bath and cool completely on a rack.
Once cool, refrigerate the cheesecake in the pan for at least 2 hours before serving. If desired, mix a bit of Chambord into the remaining sauce to thin it for serving. Garnish plates with sauce, fresh berries, and mint leaves.