Recently, major AI providers such as Google and OpenAI have introduced Finetuning-as-a-Service (FaaS), which allows users to customize Large Language Models (LLMs) using their own data. However, this service is vulnerable to safety degradation when user data includes harmful prompts, a threat known as harmful finetuning attacks. Prior works attempt to mitigate this issue by first constructing safety-aligned model and then finetuning the model on user data. However, we observe that the safety-aligned weights provide weak initialization for downstream task learning, leading to suboptimal safety-alignment and downstream task performance. To address this, we propose a Refusal-Teacher (Ref-Teacher)-guided finetuning framework. Instead of finetuning a safety-aligned model on user data, our approach directly finetunes the base model under the guidance of a safety-aligned Ref-Teacher, which filters harmful prompts from user data and distills safety-alignment knowledge into the base model. Extensive experiments demonstrate that our Ref-Teacher-guided finetuning strategy effectively minimizes harmful outputs and enhances finetuning accuracy for user-specific tasks, offering a practical solution for secure and reliable deployment of LLMs in FaaS.