In multiple input and multiple output synthetic aperture radar (MIMO-SAR) the unwanted cross-correlation output sexist inevitably in the superposed echoes of multiple transmitted orthogonal waveforms in the same frequency coverage, which may deteriorate the quality of the reconstructed SAR image because of the high synthetic integrated sidelobe level (SISL). In this study, a novel signal decomposition based on oblique projection (SDOP) method is proposed to suppress the cross-correlation outputs. At first, the superposed echo of each receiver is modelled as a linear-combined vector of transmitted multiple waveforms. Then, the echo of each transmitted waveform is obtained by signal decomposition on the combined vector via SDOP, respectively. Besides, two new metrics, that is, synthetics integrated sidelobe level ratio improved factor and integrated sidelobe level ratio loss factor, are also proposed to assess the separation performance. It is found that the cross-correlation can be effectively suppressed among multiple waveforms via low-complexity projection operators and the output signal noise ratio can be remarkably improved, accordingly. Finally, the numerical experiments are also provided to demonstrate the effectiveness of the proposed method.