In cluttered electromagnetic environments, radar is often disturbed by varied clutter, making target detection challenging. Therefore, achieving effective clutter suppression is crucial for radar target detection. However, traditional clutter suppression methods face three key challenges: (1) significant degradation in target signal detection performance when the clutter’s Doppler spectrum completely masks the target signal; (2) heavy reliance on prior knowledge for optimal performance; and (3) inherent signal energy loss during clutter suppression. To address these challenges, we propose a clutter suppression scheme based on blind source separation (BSS). Initially, the scheme utilizes parallel principal skewness analysis (PPSA) to process the echo signals in the range domain, which helps in identifying the position of moving targets. Subsequently, PPSA is applied once more to process the moving targets in the Doppler domain, allowing for the precise determination of their relative velocities. Subsequently, we evaluate the scheme’s performance with simulated and real data, comparing it with traditional clutter suppression methods and other BSS techniques. The results confirm the effectiveness of the scheme in clutter suppression.