The two-stage capacitated facility location problem (TSCFLP) aims to simultaneously determine the locations of plants and depots with limited capacities and the product flows from plants to depots and then to single source customers minimizing the total facility opening and transportation costs. In this paper, based on a cut-and-solve strategy for tree searching, a hybrid approach combining cutting plane techniques, local branching and kernel search is proposed to optimally solve the TSCFLP. In each iteration of the approach, a three-stage cutting plane method is first applied to obtain a tight lower bound and a local branching method is adopted to partition the problem into two disjoint subproblems based on the corresponding lower bound solution. The subproblem with a relatively small solution space is then exactly solved and pruned with the help of a kernel search technique. To evaluate the efficiency and the effectiveness of the proposed approach, extensive experiments on benchmark and newly generated instances of TSCFLP, as well as instances of a single-source capacitated facility location problem that is a reduced TSCFLP, are conducted. The experimental results show that our proposed approach significantly outperforms existing methods in the literature.