The mechanics that govern the constriction of the contractile ring remain poorly understood yet are critical to understanding the forces that drive cytokinesis. We used laser ablation in fission yeast cells to unravel these mechanics focusing on the role of Cdc15p as a putative anchoring protein. Our work shows that the severed constricting contractile ring recoils to a finite point leaving a gap that can heal if less than ∼1 µm. Severed contractile rings in Cdc15p-depleted cells exhibit an exaggerated recoil, which suggests that the recoil is limited by the anchoring of the ring to the plasma membrane. Based on a physical model of the severed contractile ring, we propose that Cdc15p impacts the stiffness of the contractile ring more than the viscous drag.