We address the problem of terrain-scattered jammer suppression in multiple-input multiple-output (MIMO) radar using space-(fast) time adaptive processing (SFTAP). The correlation function of jamming components after matched filtering at the receiving end of MIMO radar is derived, and its relationship to the correlation matrix of the transmitted waveforms is established. This correlation function serves as a theoretical measure of evaluating the matched filtering effect on the received jamming signals. We propose a minimum variance distortionless response (MVDR) type SFTAP design by taking into account the factors of waveform-introduced range sidelobes and cold clutter stationarity over different pulse intervals. A closed-form solution to this design is derived by means of the method of Lagrange multipliers. We also propose a relaxed SFTAP design by modifying the constraints of the MVDR type design. Both proposed SFTAP designs can support further slow-time Doppler processing procedure. Simulation results show the validity of our SFTAP designs.