Robot manipulation involves localized changes: picking up a cup moves the cup while leaving the surrounding scene largely unchanged. Yet existing 3D visual pretraining methods, including recent dynamics-aware variants, model state transitions at the scene level, compressing the motion of everything in a scene into a single global latent action. This conflates semantically distinct transitions in scenes with multiple moving parts, obscures dependencies between changing regions, and leaves the learned representation vulnerable to task-irrelevant scene content. We introduce DynaSlots, an action-free, label-free pretraining framework that decomposes each point cloud frame into a small set of temporally consistent slots and models dynamics at this per-slot level rather than the scene level. A temporal slot propagation module promotes consistent slot assignments across frames; an inverse dynamics model then extracts one latent action per slot from feature differences, and a diffusion-based forward dynamics model, paired with a self-supervised interaction head, predicts each slot's future state while learning pairwise proximity-and-motion relations. Experiments on Meta-World, Adroit, and a RealMan RM65-B robot demonstrate that DynaSlots outperforms prior scene-level baselines. It achieves superior success rates in simulation and exhibits strong robustness to scene clutter and unseen objects in real-world manipulation. Code is available at https://zhucezhanghao12345-source.github.io/DynaSlots-Anonymous/.