Clutter filtering significantly affects the sensitivity of ultrafast Doppler imaging for blood flow. The commonly used clutter filtering method is the singular value decomposition (SVD) based method, which can separate tissue clutter and blood flow signal quickly by utilizing the difference in spatiotemporal coherence of components. However, the subspaces of blood flow and noise often overlap, and thus limits SVD's capability to extract the small flow signal from noise, especially in the deep area. Considering the morphology sparsity of small vessels, we propose a Cauchy-norm-based sparse SVD (S-SVD) method to suppress the noise through combination of SVD and a sparse penalty strategy. To accelerate computation, a randomized spatial downsampling step is performed to divide the raw data into submatrices for parallel computation. We validated the effectiveness of the proposed method on in-vivo rat brain datasets. The results illustrated that the S-SVD approach can enhance ultrafast Doppler blood flow imaging in terms of sensitivity, contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR).