Accurate 3D scene motion perception significantly enhances the safety and reliability of an autonomous driving system. Benefiting from its all-weather operational capability and unique perceptual properties, 4D mmWave radar has emerged as an essential component in advanced autonomous driving. However, sparse and noisy radar points often lead to imprecise motion perception, leaving autonomous vehicles with limited sensing capabilities when optical sensors degrade under adverse weather conditions. In this paper, we propose RadarMP, a novel method for precise 3D scene motion perception using low-level radar echo signals from two consecutive frames. Unlike existing methods that separate radar target detection and motion estimation, RadarMP jointly models both tasks in a unified architecture, enabling consistent radar point cloud generation and pointwise 3D scene flow prediction. Tailored to radar characteristics, we design specialized self-supervised loss functions guided by Doppler shifts and echo intensity, effectively supervising spatial and motion consistency without explicit annotations. Extensive experiments on the public dataset demonstrate that RadarMP achieves reliable motion perception across diverse weather and illumination conditions, outperforming radar-based decoupled motion perception pipelines and enhancing perception capabilities for full-scenario autonomous driving systems.