This paper introduces CoTAEVAL, an evaluation framework to assess the effectiveness of copyright takedown methods for language models (LMs). The study explores various strategies, including system prompts, decoding-time filtering, and unlearning approaches, to prevent LM-generated content from being too similar to specific copyrighted material. The research highlights that no tested method excels across all metrics, indicating significant room for research in this area. The evaluation considers both memorization and retrieval-augmented generation (RAG) scenarios, assessing the impact on the model's ability to retain uncopyrightable factual knowledge and its general utility and efficiency. The findings suggest that while some methods reduce undesirable regurgitation, they often compromise factual knowledge or efficiency. The study emphasizes the need for further research to develop more effective takedown methods and address unresolved challenges in live policy proposals. The paper also discusses the legal and ethical implications of copyright takedown for LMs, noting the conceptual similarity to DMCA takedown but legal distinction. The evaluation framework, CoTAEVAL, provides a benchmark for assessing the feasibility and side effects of copyright takedown methods, highlighting the importance of balancing risk reduction with utility preservation. The results show that while some methods offer partial mitigation, none are perfect, and further research is needed to improve takedown effectiveness.This paper introduces CoTAEVAL, an evaluation framework to assess the effectiveness of copyright takedown methods for language models (LMs). The study explores various strategies, including system prompts, decoding-time filtering, and unlearning approaches, to prevent LM-generated content from being too similar to specific copyrighted material. The research highlights that no tested method excels across all metrics, indicating significant room for research in this area. The evaluation considers both memorization and retrieval-augmented generation (RAG) scenarios, assessing the impact on the model's ability to retain uncopyrightable factual knowledge and its general utility and efficiency. The findings suggest that while some methods reduce undesirable regurgitation, they often compromise factual knowledge or efficiency. The study emphasizes the need for further research to develop more effective takedown methods and address unresolved challenges in live policy proposals. The paper also discusses the legal and ethical implications of copyright takedown for LMs, noting the conceptual similarity to DMCA takedown but legal distinction. The evaluation framework, CoTAEVAL, provides a benchmark for assessing the feasibility and side effects of copyright takedown methods, highlighting the importance of balancing risk reduction with utility preservation. The results show that while some methods offer partial mitigation, none are perfect, and further research is needed to improve takedown effectiveness.