A surgical world model capable of generating realistic surgical action videos with precise control over tool-tissue interactions can address fundamental challenges in surgical AI and simulation -- from data scarcity and rare event synthesis to bridging the sim-to-real gap for surgical automation. However, current video generation methods, the very core of such surgical world models, require expensive annotations or complex structured intermediates as conditioning signals at inference, limiting their scalability. Other approaches exhibit limited temporal consistency across complex laparoscopic scenes and do not possess sufficient realism. We propose Surgical Action World (SAW) -- a step toward surgical action world modeling through video diffusion conditioned on four lightweight signals: language prompts encoding tool-action context, a reference surgical scene, tissue affordance mask, and 2D tool-tip trajectories. We design a conditional video diffusion approach that reformulates video-to-video diffusion into trajectory-conditioned surgical action synthesis. The backbone diffusion model is fine-tuned on a custom-curated dataset of 12,044 laparoscopic clips with lightweight spatiotemporal conditioning signals, leveraging a depth consistency loss to enforce geometric plausibility without requiring depth at inference. SAW achieves state-of-the-art temporal consistency (CD-FVD: 199.19 vs. 546.82) and strong visual quality on held-out test data. Furthermore, we demonstrate its downstream utility for (a) surgical AI, where augmenting rare actions with SAW-generated videos improves action recognition (clipping F1-score: 20.93% to 43.14%; cutting: 0.00% to 8.33%) on real test data, and (b) surgical simulation, where rendering tool-tissue interaction videos from simulator-derived trajectory points toward a visually faithful simulation engine.