Recent advancements in LLMs unlearning have shown remarkable success in removing unwanted data-model influences while preserving the model's utility for legitimate knowledge. Despite these strides, sparse Mixture-of-Experts (MoE) LLMs--a key subset of the LLM family--have remained unexplored in the context of unlearning. As MoE LLMs are celebrated for their exceptional performance, we ask:How can unlearning be performed effectively and efficiently on MoE LLMs? Our pilot study shows that the dynamic routing nature of MoE LLMs introduces unique challenges, leading to excessive forgetting, uncontrolled knowledge erasure and substantial utility drops when existing unlearning methods are applied. To address this, we propose a novel Selected-Expert Unlearning Framework (SEUF). Through expert attribution, unlearning is concentrated on the most actively engaged experts for the specified knowledge. Concurrently, an anchor loss is applied to the router to stabilize the active state of this targeted expert, ensuring focused and controlled unlearning. SEUF is compatible with various standard unlearning algorithms. Extensive experiments demonstrate that SEUF enhances both forget quality up to 5% and model utility by 35% on MoE LLMs across various benchmarks and LLM architectures (compared to standard unlearning algorithms), while only unlearning 0.06% of the model parameters.