Narrowband and broadband indoor radar images significantly deteriorate in the presence of target dependent and independent static and dynamic clutter arising from walls. A stacked and sparse denoising autoencoder (StackedSDAE) is proposed for mitigating wall clutter in indoor radar images. The algorithm relies on the availability of clean images and corresponding noisy images during training and requires no additional information regarding the wall characteristics. The algorithm is evaluated on simulated Doppler-time spectrograms and high range resolution profiles generated for diverse radar frequencies and wall characteristics in around-the-corner radar (ACR) scenarios. Additional experiments are performed on range-enhanced frontal images generated from measurements gathered from a wideband RF imaging sensor. The results from the experiments show that the StackedSDAE successfully reconstructs images that closely resemble those that would be obtained in free space conditions. Further, the incorporation of sparsity and depth in the hidden layer representations within the autoencoder makes the algorithm more robust to low signal to noise ratio (SNR) and label mismatch between clean and corrupt data during training than the conventional single layer DAE. For example, the denoised ACR signatures show a structural similarity above 0.75 to clean free space images at SNR of -10dB and label mismatch error of 50%.