With rapid advances, generative large language models (LLMs) dominate various Natural Language Processing (NLP) tasks from understanding to reasoning. Yet, language models' inherent vulnerabilities may be exacerbated due to increased accessibility and unrestricted model training on massive textual data from the Internet. A malicious adversary may publish poisoned data online and conduct backdoor attacks on the victim LLMs pre-trained on the poisoned data. Backdoored LLMs behave innocuously for normal queries and generate harmful responses when the backdoor trigger is activated. Despite significant efforts paid to LLMs' safety issues, LLMs are still struggling against backdoor attacks. As Anthropic recently revealed, existing safety training strategies, including supervised fine-tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF), fail to revoke the backdoors once the LLM is backdoored during the pre-training stage. In this paper, we present Simulate and Eliminate (SANDE) to erase the undesired backdoored mappings for generative LLMs. We initially propose Overwrite Supervised Fine-tuning (OSFT) for effective backdoor removal when the trigger is known. Then, to handle the scenarios where the trigger patterns are unknown, we integrate OSFT into our two-stage framework, SANDE. Unlike previous works that center on the identification of backdoors, our safety-enhanced LLMs are able to behave normally even when the exact triggers are activated. We conduct comprehensive experiments to show that our proposed SANDE is effective against backdoor attacks while bringing minimal harm to LLMs' powerful capability without any additional access to unbackdoored clean models. We will release the reproducible code.