Cognitive multiple-input multiple-output (MIMO) radar is capable of adjusting system parameters adaptively by sensing and learning in complex dynamic environment. Beamforming performance of MIMO radar is guided by both beamforming weight coefficients and the transceiver configuration. We propose a cognitive-driven MIMO array design where both the beamforming weights and the transceiver configuration are adaptively and concurrently optimized under different environmental conditions. The perception-action cycle involves data collection of full virtual array, covariance reconstruction and joint design of the transmit and receive arrays by antenna selection.The optimal transceiver array design is realized by promoting two-dimensional group sparsity via iteratively minimizing reweighted mixed L21-norm, with constraints imposed on transceiver antenna spacing for proper transmit/receive isolation. Simulations are provided to demonstrate the "perception-action" capability of the proposed cognitive sparse MIMO array in achieving enhanced beamforming and anti-jamming in dynamic target and interference environment.