In recent years, the rapid development of marine science has put forward higher and higher requirements for the processing of ship-radiated noise signal. Ship-radiated noise is the noise signal generated by the vibration of various mechanical equipment or the movement of the hull and radiated into the sea when the ship is traveling. Ship-radiated noise signal contains a large number of time-varying, nonlinear and non-stationary components. The denoising processing of ship-radiated noise is the most critical part of underwater acoustic signal processing. In order to more effective reduce the noise of the ship-radiated noise signal, a new denoising method for underwater acoustic signal based on mutual information variational mode decomposition (MIVMD), multivariate multiscale dispersion entropy (mvMDE), and lift wavelet threshold (LWTD) and Savitzky Golay filter (S-G filter), named MIVMD-mvMDE-LWTD-SG, is proposed. Firstly, MIVMD is used to decompose the original signal into n subsignals. Secondly, the mvMDE value of each sub-signal is calculated, and the n sub-signals are divided into high-frequency components and low-frequency components according to the threshold. Then, S-G filter and LWTD method are used to reduce the noise of low-frequency components and high-frequency components respectively. Finally, the low-frequency components and high-frequency components after the denoising processing are reconstructed to obtain the denoising signal. In order to verify the effectiveness of the proposed method, the proposed method is used to reduce the noise of chaotic signal under different signalto-noise ratios (SNR), and compared with the EMD-mvMDE-LWTD and MIVMD-mvMDE-LWTD method. The results show that the proposed method can effective remove the noise in the chaotic signal, better distinguish the adjacent trajectories in the phase space, approximate the real chaotic attractor trajectory, and better retain the useful information in the chaotic signal. The proposed method is further applied to the actual ship-radiated noise signal, and the experimental analysis shows its effectiveness, which lays a solid foundation for further prediction and detection. INDEX TERMS Mutual information variational mode decomposition; multivariate multiscale dispersion entropy; lift wavelet threshold; chaotic signal; denoising