Ensuring the proper use of sensitive data in analytics under complex privacy policies is an increasingly critical challenge. Many existing approaches lack portability, verifiability, and scalability across diverse data processing frameworks. We introduce Picachv, a novel security monitor that automatically enforces data use policies. It works on relational algebra as an abstraction for program semantics, enabling policy enforcement on query plans generated by programs during execution. This approach simplifies analysis across diverse analytical operations and supports various front-end query languages. By formalizing both data use policies and relational algebra semantics in Coq, we prove that Picachv correctly enforces policies. Picachv also leverages Trusted Execution Environments (TEEs) to enhance trust in runtime, providing provable policy compliance to stakeholders that the analytical tasks comply with their data use policies. We integrated Picachv into Polars, a state-of-the-art data analytics framework, and evaluate its performance using the TPC-H benchmark. We also apply our approach to real-world use cases. Our work demonstrates the practical application of formal methods in securing data analytics, addressing key challenges.