A truly generalizable approach to rigid segmentation and motion estimation is fundamental to 3D understanding of articulated objects and moving scenes. In view of the closely intertwined relationship between segmentation and motion estimates, we present an SE(3) equivariant architecture and a training strategy to tackle this task in an unsupervised manner. Our architecture is composed of two interconnected, lightweight heads. These heads predict segmentation masks using point-level invariant features and estimate motion from SE(3) equivariant features, all without the need for category information. Our training strategy is unified and can be implemented online, which jointly optimizes the predicted segmentation and motion by leveraging the interrelationships among scene flow, segmentation mask, and rigid transformations. We conduct experiments on four datasets to demonstrate the superiority of our method. The results show that our method excels in both model performance and computational efficiency, with only 0.25M parameters and 0.92G FLOPs. To the best of our knowledge, this is the first work designed for category-agnostic part-level SE(3) equivariance in dynamic point clouds.