Mutation-based Fault Localization (MBFL) has been widely explored for automated software debugging, leveraging artificial mutants to identify faulty code entities. However, MBFL faces significant challenges due to interference mutants generated from non-faulty code entities but can be killed by failing tests. These mutants mimic the test sensitivity behaviors of real faulty code entities and weaken the effectiveness of fault localization. To address this challenge, we introduce the concept of Fault Localization Interference Mutants (FLIMs) and conduct a theoretical analysis based on the Reachability, Infection, Propagation, and Revealability (RIPR) model, identifying four distinct interference causes. Building on this, we propose a novel approach to semantically recognize and mitigate FLIMs using LLM-based semantic analysis, enhanced by fine-tuning techniques and confidence estimation strategies to address LLM output instability. The recognized FLIMs are then mitigated by refining the suspiciousness scores calculated from MBFL techniques. We integrate FLIM recognition and mitigation into the MBFL workflow, developing MBFL-FLIM, a fault localization framework that enhances MBFL's effectiveness by reducing misleading interference while preserving real fault-revealing information. Our empirical experiments on the Defects4J benchmark with 395 program versions using eight LLMs demonstrate MBFL-FLIM's superiority over traditional SBFL and MBFL methods, advanced dynamic feature-based approaches, and recent LLM-based fault localization techniques. Specifically, MBFL-FLIM achieves an average improvement of 44 faults in the Top-1 metric, representing a significant enhancement over baseline methods. Further evaluation confirms MBFL-FLIM's robust performance in multi-fault scenarios, with ablation experiments validating the contributions of the fine-tuning and confidence estimation components.