Fine-tuning pre-trained Large Language Models (LLMs) for specialized tasks incurs substantial computational and data costs. While model merging offers a training-free solution to integrate multiple task-specific models, existing methods suffer from safety-utility conflicts where enhanced general capabilities degrade safety safeguards. We identify two root causes: \textbf{neuron misidentification} due to simplistic parameter magnitude-based selection, and \textbf{cross-task neuron interference} during merging. To address these challenges, we propose \textbf{LED-Merging}, a three-stage framework that \textbf{L}ocates task-specific neurons via gradient-based attribution, dynamically \textbf{E}lects critical neurons through multi-model importance fusion, and \textbf{D}isjoints conflicting updates through parameter isolation. Extensive experiments on Llama-3-8B, Mistral-7B, and Llama2-13B demonstrate that LED-Merging reduces harmful response rates(\emph{e.g.}, a 31.4\% decrease on Llama-3-8B-Instruct on HarmBench) while preserving 95\% of utility performance(\emph{e.g.}, 52.39\% accuracy on GSM8K). LED-Merging resolves safety-utility conflicts and provides a lightweight, training-free paradigm for constructing reliable multi-task LLMs.