Large language models (LLMs) still suffer from the issue of hallucination. Post-editing the hallucinated text generated by LLMs via external knowledge sources has become a popular approach. However, two challenges still remain: multi-hop hallucination mitigation and non-authoritative knowledge sources. The former refers to the gathering of multiple pieces of evidence and utilization of multi-hop reasoning when mitigating hallucination. The latter indicates the possibility that external knowledge sources themselves may contain irrelevant or incorrect information. To address these challenges, we propose the multi-hop hallucination mitigation task in three practical external knowledge source settings: relevant, irrelevant and conflict. To facilitate further research on this task, we construct two high-quality datasets, namely HoCurr and HotpotEC. To better deal with this task in various settings, we propose a method called FixER, in which a BaseFix iteratively enhances its performance with the assistance of a carefully designed Evaluator and Reflector. Experiments demonstrate that our proposed task is highly challenging and our method is effective comparing with the baselines.