Anatomical structures are rarely static during a surgical procedure due to breathing, heartbeats, and peristaltic movements. Inspired by observing an expert surgeon, we propose an intermittent synchronization with the extrema of the rhythmic motion (i.e., the lowest velocity windows). We performed 2 experiments: (1) pattern cutting, and (2) debridement. In (1), we found that the intermittent synchronization approach, while 1.8x slower than tracking motion, was significantly more robust to noise and control latency, and it reduced the max cutting error by 2.6x In (2), a baseline approach with no synchronization achieves 62% success rate for each removal, while intermittent synchronization achieves 80%.