What is a very tart red berry used for sauce or juice?

The most likely answer you're looking for is a cranberry.

Cranberries are known for their tart flavor and are commonly used in sauces, juices, and even relishes.

Other possibilities include:

* Sour cherries: These are also quite tart and can be used for sauces and juices.

* Barberries: While less common, these small red berries have a very tart flavor and are used in some Persian dishes.

Let me know if you have any more clues or details about the berry!