Robotic-assisted minimally invasive surgery (MIS) has enabled procedures with increased precision and dexterity, but surgical robots are still open loop and require surgeons to work with a tele-operation console providing only limited visual feedback. In this setting, mechanical failures, software faults, or human errors might lead to adverse events resulting in patient complications or fatalities. We argue that impending adverse events could be detected and mitigated by applying context-specific safety constraints on the motions of the robot. We present a context-aware safety monitoring system which segments a surgical task into subtasks using kinematics data and monitors safety constraints specific to each subtask. To test our hypothesis about context specificity of safety constraints, we analyze recorded demonstrations of dry-lab surgical tasks collected from the JIGSAWS database as well as from experiments we conducted on a Raven II surgical robot. Analysis of the trajectory data shows that each subtask of a given surgical procedure has consistent safety constraints across multiple demonstrations by different subjects. Our preliminary results show that violations of these safety constraints lead to unsafe events, and there is often sufficient time between the constraint violation and the safety-critical event to allow for a corrective action.