Layover separation has been fundamental to many synthetic aperture radar applications, such as building reconstruction and biomass estimation. Retrieving the scattering profile along the mixed dimension (elevation) is typically solved by inversion of the SAR imaging model, a process known as SAR tomography. This paper proposes a nonlinear blind scatterer separation method to retrieve the phase centers of the layovered scatterers, avoiding the computationally expensive tomographic inversion. We demonstrate that conventional linear separation methods, e.g., principle component analysis (PCA), can only partially separate the scatterers under good conditions. These methods produce systematic phase bias in the retrieved scatterers due to the nonorthogonality of the scatterers' steering vectors, especially when the intensities of the sources are similar or the number of images is low. The proposed method artificially increases the dimensionality of the data using kernel PCA, hence mitigating the aforementioned limitations. In the processing, the proposed method sequentially deflates the covariance matrix using the estimate of the brightest scatterer from kernel PCA. Simulations demonstrate the superior performance of the proposed method over conventional PCA-based methods in various respects. Experiments using TerraSAR-X data show an improvement in height reconstruction accuracy by a factor of one to three, depending on the used number of looks.