Belief Peaks Clustering （BPC） algorithm is a new variant of Density Peaks Clustering （DPC） algorithm based on fuzzy perspective. It uses fuzzy mathematics to describe the distribution characteristics and correlation of data. However， BPC algorithm mainly relies on the information of local data points in the calculation of belief values， instead of investigating the distribution and structure of the whole dataset. Moreover， the robustness of the original allocation strategy is weak. To solve these problems， a fuzzy Clustering algorithm based on Belief Subcluster Cutting （BSCC） was proposed by combining belief peaks and spectral method. Firstly， the dataset was divided into many high-purity subclusters by local belief information. Then， the subcluster was regarded as a new sample， and the spectral method was used for cutting graph clustering through the similarity relationship between clusters， thus coupling local information and global information. Finally， the points in the subcluster were assigned to the class cluster where the subcluster was located to complete the final clustering. Compared with BPC algorithm， BSCC has obvious advantages on datasets with multiple subclusters， and it has the ACCuracy （ACC） improvement of 16.38 and 21.35 percentage points on americanflag dataset and Car dataset， respectively. Clustering experimental results on synthetic datasets and real datasets show that BSCC outperforms BPC and the other seven clustering algorithms on the three evaluation indicators of Adjusted Rand Index （ARI）， Normalized Mutual Information （NMI） and ACC.