We examine the kinematic morphology of early-type galaxies ( ETGs ) in eight galaxy clusters in the Sydney-AAO Multi-object Integral field spectrograph ( SAMI ) Galaxy Survey . The clusters cover a mass range of 14.2 < \log ( M _ { 200 } / M _ { \odot } ) < 15.2 and we measure spatially-resolved stellar kinematics for 315 member galaxies with stellar masses 10.0 < \log ( M _ { * } / M _ { \odot } ) \leq 11.7 within 1 R _ { 200 } of the cluster centers . We calculate the spin parameter , \lambda _ { R } and use that to classify the kinematic morphology of the galaxies as fast or slow rotators . The total fraction of slow rotators in the early-type galaxy population , F _ { SR } = 0.14 \pm { 0.02 } and does not depend on host cluster mass . Across the eight clusters , the fraction of slow rotators increases with increasing local overdensity . We also find that the slow-rotator fraction increases at small clustercentric radii ( R _ { cl } < 0.3 R _ { 200 } ) , and note that there is also an increase in slow-rotator fraction at R _ { cl } \sim 0.6 R _ { 200 } . The slow rotators at these larger radii reside in cluster substructure . We find the strongest increase in slow-rotator fraction occurs with increasing stellar mass . After accounting for the strong correlation with stellar mass , we find no significant relationship between spin parameter and local overdensity in the cluster environment . We conclude that the primary driver for the kinematic morphology–density relationship in galaxy clusters is the changing distribution of galaxy stellar mass with local environment . The presence of slow rotators in substructure suggests that the cluster kinematic morphology–density relationship is a result of mass segregation of slow-rotating galaxies forming in groups that later merge with clusters and sink to the cluster center via dynamical friction .