The flying ad hoc networks (FANETs) have attracted a large amount of attention from both academia and industry. Benefiting from the flexibility, the FANETs have been widely deployed in various scenarios, ranging from agricultural production to emergency rescue. However, in FANETs, the mobility of unmanned aerial vehicles (UAVs) has led to critical challenges for the stability of communications. Especially, the routing flooding mechanism extremely limits the scalability of FANET. To overcome these technical challenges, constructing a hierarchy and clustering structure in FANETs is considered a promising solution. In this paper, we propose the fission spectral clustering (FSC) strategy for UAV swarm networks. We model the UAV clustering problem as a graph cut problem. The time-sequential attributes weight of nodes and edges will be input to the FSC algorithm. Then, it will construct the Laplace matrix and calculate the first k-th eigenvectors of it. We apply the K-Means algorithm into this feature space to cut the graph by clustering the eigenvectors. Each cluster will constantly fission with this strategy until it satisfies the size and structure constraints in the UAV clusters. Some simulations are implemented to evaluate our proposed algorithm in comparison to the other state-of-the-art solutions.