Refusal-Aware Instruction Tuning (RAIT) aims to enhance Large Language Models (LLMs) by improving their ability to refuse responses to questions beyond their knowledge, thereby reducing hallucinations and improving reliability. Effective RAIT must address two key challenges: firstly, effectively reject unknown questions to minimize hallucinations; secondly, avoid over-refusal to ensure questions that can be correctly answered are not rejected, thereby maintain the helpfulness of LLM outputs. In this paper, we address the two challenges by deriving insightful observations from the gradient-based perspective, and proposing the Gradient-driven Refusal Aware Instruction Tuning Framework GRAIT: (1) employs gradient-driven sample selection to effectively minimize hallucinations and (2) introduces an adaptive weighting mechanism during fine-tuning to reduce the risk of over-refusal, achieving the balance between accurate refusals and maintaining useful responses. Experimental evaluations on open-ended and multiple-choice question answering tasks demonstrate that GRAIT significantly outperforms existing RAIT methods in the overall performance. The source code and data will be available at https://github.com/opendatalab/GRAIT .