Motion Object Segmentation (MOS) is crucial for autonomous driving, as it enhances localization, path planning, map construction, scene flow estimation, and future state prediction. While existing methods achieve strong performance, balancing accuracy and real-time inference remains a challenge. To address this, we propose a logits-based knowledge distillation framework for MOS, aiming to improve accuracy while maintaining real-time efficiency. Specifically, we adopt a Bird's Eye View (BEV) projection-based model as the student and a non-projection model as the teacher. To handle the severe imbalance between moving and non-moving classes, we decouple them and apply tailored distillation strategies, allowing the teacher model to better learn key motion-related features. This approach significantly reduces false positives and false negatives. Additionally, we introduce dynamic upsampling, optimize the network architecture, and achieve a 7.69% reduction in parameter count, mitigating overfitting. Our method achieves a notable IoU of 78.8% on the hidden test set of the SemanticKITTI-MOS dataset and delivers competitive results on the Apollo dataset. The KDMOS implementation is available at https://github.com/SCNU-RISLAB/KDMOS.