Recent experiments show that a thin film anode on a compliant substrate can significantly mitigate mechanical degradation and capacity fading of lithium-ion and sodium-ion batteries in service. The enhanced cycle performance of such a substrate-supported thin film anode is attributed to the wrinkling-induced stress relaxation. While the experimental evidence is suggestive, there lacks a systematic mechanistic study of the wrinkling of the substrate-supported thin film anode and its influence on anode cycle performance. We report a comprehensive study of the charging/discharging induced wrinkling formation and subsequent morphologic evolution of a substrate-supported thin film anode, using theoretical analysis and finite element simulations. We reveal that necking bands may form near wrinkling troughs or peaks and further develop to cause fragmentation of the anode over charging/discharging cycles, a failure mode not reported in the existing literature. The density and distribution of the wrinkling-associated necking bands in the substrate-supported thin film anode can be regulated by the substrate stiffness. Moreover, the wrinkling-induced necking in such a thin film anode can be deferred by regulating the charging capacity. These findings offer new mechanistic understanding of substrate-supported thin film anodes and thus shed light on novel design of high performance anodes in batteries.