The actin regulatory protein, cofilin, increases the bending and twisting elasticity of actin filaments and severs them. It has been proposed that filaments partially decorated with cofilin accumulate stress from thermally driven shape fluctuations at bare (stiff) and decorated (compliant) boundaries, thereby promoting severing. This mechanics-based severing model predicts that changes in actin filament compliance due to cofilin binding affect severing activity. Here, we test this prediction by evaluating how the severing activities of vertebrate and yeast cofilactin scale with the flexural rigidities determined from analysis of shape fluctuations. Yeast actin filaments are more compliant in bending than vertebrate actin filaments. Severing activities of cofilactin isoforms correlate with changes in filament flexibility. Vertebrate cofilin binds but does not increase the yeast actin filament flexibility, and does not sever them. Imaging of filament thermal fluctuations reveals that severing events are associated with local bending and fragmentation when deformations attain a critical angle. The critical severing angle at boundaries between bare and cofilin-decorated segments is smaller than in bare or fully decorated filaments. These measurements support a cofilin-severing mechanism in which mechanical asymmetry promotes local stress accumulation and fragmentation at boundaries of bare and cofilin-decorated segments, analogous to failure of some nonprotein materials.