High-frequency surface-wave radar (HFSWR) is widely used in vessel and aircraft detection, sea-state sensing and wind-field mapping. Target detection suffers from the ionospheric clutter, which is reflected by the ionosphere. Adaptive beamforming (ABF) has been used for ionospheric clutter mitigation. However, the performance of ABF is limited by the heterogeneous ionospheric clutter and degrees of freedom (DOF) of the antennas array. In order to improve the performance, here, the one-dimensional ABF is expanded to two-dimensional fast-time space–time adaptive processing (STAP), which combines beam and range domains to obtain more DOFs than that in the ABF. In addition, the blind sources separation (BSS) method is also used to improve the spatial covariance matrix estimation accuracy of STAP in the heterogeneous ionospheric clutter background. The simulation and real data results demonstrate the effectiveness of the proposed BSS-STAP method in HFSWR.