Modern deep learning models have high memory and computation cost. To make them fast and memory-cost efficient, structured model pruning is commonly used. We find that pruning a model using a common training accelerator with large systolic arrays is extremely performance-inefficient. To make a systolic array efficient for pruning and training, we propose FlexSA, a flexible systolic array architecture. FlexSA dynamically reconfigures the systolic array structure and offers multiple sub-systolic operating modes, which are designed for energy- and memory bandwidth-efficient processing of tensors with different sizes and shapes. We also present a compilation heuristic for tiling matrix-multiplication-and-accumulation operations in a training workload to best utilize the resources of FlexSA. Based on our evaluation, FlexSA with the proposed compilation heuristic improves compute resource utilization of pruning and training modern CNN models by 37% compared to a conventional training accelerator with a large systolic array. FlexSA also improves on-chip data reuse by 1.7X saving 28% energy compared to naive systolic array splitting.