Ensuring robust safety alignment while preserving utility is critical for the reliable deployment of Large Language Models (LLMs). However, current techniques fundamentally suffer from intertwined deficiencies: insufficient robustness against malicious attacks, frequent refusal of benign queries, degradation in generated text quality and general task performance--the former two reflecting deficits in robust safety and the latter constituting utility impairment. We trace these limitations to the coarse-grained layer-wise interventions in existing methods. To resolve this, we propose NeuronTune, a fine-grained framework that dynamically modulates sparse neurons to achieve simultaneous safety-utility optimization. Our approach first identifies safety-critical and utility-preserving neurons across all layers via attribution, then employs meta-learning to adaptively amplify safety-neuron activations and suppress utility-neuron activations. Crucially, NeuronTune enables tunable adjustment of intervention scope via neuron-count thresholds, supporting flexible adaptation to security-critical or utility-priority scenarios. Extensive experimental results demonstrate that our method significantly outperforms existing state-of-the-art technologies, achieving superior model safety while maintaining excellent utility.