Ground-Penetrating Radar (GPR) is a non-destructive sensing technology that utilizes high electromagnetic frequencies. However, mutual interference waves caused by multiple scattering between targets can significantly complicate the interpretation of GPR B-scan images, especially when shallow targets obscure deeper ones. Existing methods primarily focus on extracting target signals from background clutter, frequently overlooking the impact of mutual interference. This paper proposes a convolutional neural network, termed MIS-SE-Net (Mutual Interference Suppression and Signal Enhancement Network), designed to suppress mutual interference waves while preserving shallow target signals and enhancing deeper ones. MIS-SE-Net incorporates attention gates into its encoder–decoder architecture, thereby improving its capabilities in interference suppression and enhancement of weak signals. The network is optimized using a combination of Mean Absolute Error (MAE) loss and perceptual loss. To evaluate MIS-SE-Net, the multi-scale weighted back projection (MWBP) imaging algorithm is used. Simulation results show that after processing with MIS-SE-Net, the integrated side-lobe ratio (ISLR) metric of MWBP imaging decreases by an average of 2.37%, while the signal-to-clutter ratio (SCR) increases by an average of 1.65%. For measured data, results show an average decrease of 7.51% in ISLR and an increase of 2.47% in SCR. These findings validate the effectiveness of the proposed method in suppressing interference, enhancing weak signals, and improving imaging quality.