In a medium saucepan, combine the raspberries, blackberries, sugar, vinegar, and water. Bring the mixture to a boil over medium heat, stirring occasionally.

In a small bowl, mix together the cornstarch and 1 tablespoon of water to create a slurry. Pour the slurry into the saucepan with the berry mixture, and stir until well combined.

Reduce the heat to low and simmer the sauce for 10-15 minutes, or until the berries have broken down and the sauce has thickened.

Remove the saucepan from the heat and let the sauce cool for a few minutes. Then, use an immersion blender or a regular blender to puree the sauce until smooth.

Pour the sauce through a fine-mesh strainer to remove any seeds or bits of berry skin. Discard the solids and transfer the sauce to a clean jar or container.

Store the sauce in the refrigerator until ready to use. It will keep for up to a week.