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, is significantly more robust to noise and control latency, and it reduces the max cutting error by 2.6X except when motion is along 3 or more orthogonal axes. In (2), a baseline approach with no synchronization succeeds in 62% of debridement attempts while intermittent synchronization achieves an 80% success rate.