Owing to the promising ability of saving hardware cost and spectrum resources, integrated sensing and communication (ISAC) is regarded as a revolutionary technology for future sixth-generation (6G) networks. The mono-static ISAC systems considered in most of existing works can only achieve limited sensing performance due to the single observation angle and easily blocked transmission links, which motivates researchers to investigate cooperative ISAC networks. In order to further improve the degrees of freedom (DoFs) of cooperative ISAC networks, the transmitter-receiver selection, i.e., base station (BS) mode selection problem, is meaningful to be studied. However, to our best knowledge, this crucial problem has not been extensively studied in existing works. In this paper, we consider the joint BS mode selection, transmit beamforming, and receive filter designs for cooperative cell-free ISAC networks, where multi-BSs cooperatively serve communication users and detect targets. An efficient joint beamforming design algorithm and three different heuristic BS mode selection methods are proposed to solve the non-convex NP-hard problem. Simulation results demonstrates the advantages of cooperative ISAC networks, the importance of BS mode selection, and the effectiveness of proposed algorithms.