During fine-tuning, large language models (LLMs) are increasingly vulnerable to data-poisoning backdoor attacks, which compromise their reliability and trustworthiness. However, existing defense strategies suffer from limited generalization: they only work on specific attack types or task settings. In this study, we propose Poison-to-Poison (P2P), a general and effective backdoor defense algorithm. P2P injects benign triggers with safe alternative labels into a subset of training samples and fine-tunes the model on this re-poisoned dataset by leveraging prompt-based learning. This enforces the model to associate trigger-induced representations with safe outputs, thereby overriding the effects of original malicious triggers. Thanks to this robust and generalizable trigger-based fine-tuning, P2P is effective across task settings and attack types. Theoretically and empirically, we show that P2P can neutralize malicious backdoors while preserving task performance. We conduct extensive experiments on classification, mathematical reasoning, and summary generation tasks, involving multiple state-of-the-art LLMs. The results demonstrate that our P2P algorithm significantly reduces the attack success rate compared with baseline models. We hope that the P2P can serve as a guideline for defending against backdoor attacks and foster the development of a secure and trustworthy LLM community.