In many eukaryotes, cytokinesis is facilitated by the contraction of an actomyosin ring (AMR). The exact mechanisms that lead to this contractility are unknown, although some models posit that actin turnover in the AMR is essential. The effect of reduced actin dynamics during AMR formation has been well studied in Schizosaccharomyces pombe; however, the corresponding effects on AMR contraction are not well understood. By using mutants of the fission yeast actin severing protein Adf1, we observed that contracting AMRs display a "peeling" phenotype, where bundles of actin and myosin peel off from one side of the AMR, and are pulled across to the opposite side. This occurs multiple times during cytokinesis and is dependent on the activity of myosins Myo2, Myp2, and Myo51. We found that the distribution of Myo2 in the AMR anticorrelates with the location of peeling events, suggesting that peeling is caused by a nonuniform tension distribution around the AMR, and that one of the roles of actin turnover is to maintain a uniform tension distribution around the AMR.