Recent studies reveal that Large Language Models (LLMs) face challenges in balancing safety with utility, particularly when processing long texts for NLP tasks like summarization and translation. Despite defenses against malicious short questions, the ability of LLMs to safely handle dangerous long content, such as manuals teaching illicit activities, remains unclear. Our work aims to develop robust defenses for LLMs in processing malicious documents alongside benign NLP task queries. We introduce a defense dataset comprised of safety-related examples and propose single-task and mixed-task losses for instruction tuning. Our empirical results demonstrate that LLMs can significantly enhance their capacity to safely manage dangerous content with appropriate instruction tuning. Additionally, strengthening the defenses of tasks most susceptible to misuse is effective in protecting LLMs against processing harmful information. We also observe that trade-offs between utility and safety exist in defense strategies, where Llama2, utilizing our proposed approach, displays a significantly better balance compared to Llama1.