Low-power electromagnetic-acoustic transducer (EMAT) is crucially important for safety-critical equipment in industry, especially for potential explosives and inflammable petrochemical equipment and facilities. When the excitation power is very low, the corresponding echoes are overwhelmed in noise and related measurement would be inaccurate. To solve this problem, this paper presents a new echo reconstruction method based on a deep stacked denoising autoencoder (DSDAE) for nondestructive evaluation. First, the uses of reference signals and new data structure are to improve the training efficiency. A hybrid method based on variational mode decomposition and wavelet transform is used to obtain clean reference signals as inputs of the deep network. Then, the modified network structure and loss function aim to improve the ability of feature extraction and reconstruct clean echoes from low-power EMAT signals. To validate the effectiveness of the proposed method, the experiments of self-excitation and receiving A-scan inspections of stepped specimens with different thicknesses are conducted at some excitation voltages, as low as 25 V. The results indicate that the proposed DSDAE shows better and more stable denoising performance than some popular processing methods for different specimens and excitation voltages. It greatly improves the signal-to-noise ratio of the reconstructed signal to 20 dB. When applying to thickness measurement of specimens, its relative error is lower than 0.3%, which provides a practical and accurate tool for low-power EMAT testing.