Autonomous robotic surgery has seen significant progression over the last decade with the aims of reducing surgeon fatigue, improving procedural consistency, and perhaps one day take over surgery itself. However, automation has not been applied to the critical surgical task of controlling tissue and blood vessel bleeding--known as hemostasis. The task of hemostasis covers a spectrum of bleeding sources and a range of blood velocity, trajectory, and volume. In an extreme case, an un-controlled blood vessel fills the surgical field with flowing blood. In this work, we present the first, automated solution for hemostasis through development of a novel probabilistic blood flow detection algorithm and a trajectory generation technique that guides autonomous suction tools towards pooling blood. The blood flow detection algorithm is tested in both simulated scenes and in a real-life trauma scenario involving a hemorrhage that occurred during thyroidectomy. The complete solution is tested in a physical lab setting with the da Vinci Research Kit (dVRK) and a simulated surgical cavity for blood to flow through. The results show that our automated solution has accurate detection, a fast reaction time, and effective removal of the flowing blood. Therefore, the proposed methods are powerful tools to clearing the surgical field which can be followed by either a surgeon or future robotic automation developments to close the vessel rupture.