The conventional blind source separation independent component analysis method has the problem of low-separation performance. In addition, the basic butterfly optimization algorithm has the problem of insufficient search capability. In order to solve the above problems, an independent component analysis method based on the double-mutant butterfly optimization algorithm (DMBOA) is proposed in this paper. The proposed method employs the kurtosis of the signal as the objective function. By optimizing the objective function, blind source separation of the signals is realized. Based on the original butterfly optimization algorithm, DMBOA introduces dynamic transformation probability and population reconstruction mechanisms to coordinate global and local search, and when the optimization stagnates, the population is reconstructed to increase diversity and avoid falling into local optimization. The differential evolution operator is introduced to mutate at the global position update, and the sine cosine operator is introduced to mutate at the local position update, hence, enhancing the local search capability of the algorithm. To begin, 12 classical benchmark test problems were selected to evaluate the effectiveness of DMBOA. The results reveal that DMBOA outperformed the other benchmark algorithms. Following that, DMBOA was utilized for the blind source separation of mixed image and speech signals. The simulation results show that the DMBOA can realize the blind source separation of an observed signal successfully and achieve higher separation performance than the compared algorithms.