In coal and rock recognition technology, the acquisition of sound signals is affected by background noise. It is challenging to extract cutting features and accurately identify cutting patterns effectively. Therefore, this paper proposes an approach for combined noise reduction of the cutting sound signal based on the improved adaptive noise complete ensemble empirical mode decomposition (ICEEMDAN) and a singular value decomposition (SVD). First, the method used the ICEEMDAN method to decompose the noisy signal into several intrinsic mode functions (IMF). It calculated the correlation coefficient between the IMF component and the noisy signal and then selected the noisy IMF components based on the threshold formula. Meanwhile, this method constructed a Hankel matrix of the noisy IMF component signals. It used SVD technology to obtain the singular values. According to the singular value standard energy spectrum curve, the paper determined the order of the effective singular value and removed the noise component in the signal. Then, the denoised IMF and noiseless IMF components are superimposed and reconstructed to obtain the noise-reduced cutting sound signal. Finally, it applied simulation signal and simulated shearer cutting experiment to verify the performance of the method. The results show that the proposed method can effectively remove the influence of background noise in the signal and retain the characteristic frequencies of the original cutting sound signal. Compared with traditional noise reduction methods, the ICEEMDAN-SVD combined noise reduction method performs better in noise reduction evaluation standards of signal-noise ratio and root mean square error. It achieved a better noise reduction effect, which could help coal and rock recognition technology based on sound signals.