The goal of this research is the application of variational mode decomposition (VMD) in the denoising process of acoustic signals from high-voltage shunt reactors. This paper propose a unique joint denoising method that combines improved VMD and wavelet threshold. The coati optimization algorithm (COA) was introduced to optimally find the optimal combination of VMD decomposition parameters. The optimized and improved VMD was then used to decompose the original noisy reactor acoustic signal. The correlation coefficient method was introduced to remove uncorrelated intrinsic mode functions (IMFs). The wavelet threshold denoising algorithm was applied for secondary noise reduction on the extracted IMFs. The denoised IMFs were subsequently superimposed and reconstructed to obtain the denoised acoustic signal. Comprehensive comparison and analysis of these methods were conducted through simulation experiments and practical tests. The results indicate that COA-VMD-Wavelet Threshold—significantly reduces the reconstructed signal errors with high practicality and effectiveness.