In this paper, we consider a cooperative communication network where multiple satellites provide services for ground users (GUs) (at the same time and on the same frequency). The communication and computational resources on satellites are usually restricted and the satellite-GU link determination affects the communication performance significantly when multiple satellites provide services for multiple GUs in a collaborative manner. Therefore, considering the limitation of the on-board radio-frequency chains, we first propose a hybrid beamforming method consisting of analog beamforming for beam alignment and digital beamforming for interference mitigation. Then, to establish appropriate connections between satellites and GUs, we propose a heuristic user scheduling algorithm which determines the connections according to the total spectral efficiency (SE) increment of the multi-satellite cooperative network. Next, a joint hybrid beamforming and user scheduling scheme is proposed to dramatically improve the performance of the multi-satellite cooperative network. Moreover, simulations are conducted to compare the proposed schemes with representative baselines and analyze the key factors influencing the performance of the multi-satellite cooperative network. It is shown that the proposed joint beamforming and user scheduling approach can provide 47.2% SE improvement on average as compared with its non-joint counterpart.