Vibration signals have been widely used for structural response analysis and blast design guidance. Monitoring the blast vibration signals of a structure is an effective way to determine the blast vibration hazard. The blasting and collapse of high-rise structures takes place in several stages, and the vibration signals generated by the explosion and collapse of different structures overlap at different stages. Combined with the harsh measurement environment, the recorded blast vibration signal would inevitably introduce noise. The key point of reducing the noise of vibration signals is to distinguish the high-frequency signals from different sources, which is crucial for group structures demolition. In this paper, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) algorithm has been used to decompose the monitored blast vibration signals into modal functions with different characteristics. The noisy modal functions are then denoised using wavelet thresholding. The spectral relationship of the noisy signal components before and after denoising is also calculated using Welch’s method to verify the effectiveness of the denoising method. The applied method is compared with three other signal decomposition methods (Complementary ensemble empirical mode decomposition with adaptive noise, variational mode decomposition, successive variational mode decomposition) to analyse the advantages and disadvantages of different algorithms for decomposing blast vibration signals. The results show that the proposed denoise method has better performance and can be considered as an effective noise reduction method for blast vibration signal reconstruction.