Cloud radio access network (Cloud-RAN) is a promising network architecture to meet the explosive growth of the mobile data traffic. In this architecture, as all the baseband signal processing is shifted to a single baseband unit (BBU) pool, interference management can be efficiently achieved through coordinated beamforming, which, however, often requires full channel state information (CSI). In practice, the overhead incurred to obtain full CSI will dominate the available radio resource. In this paper, we propose a unified framework for the CSI overhead reduction and downlink coordinated beamforming. Motivated by the channel heterogeneity phenomena in large-scale wireless networks, we first propose a novel CSI acquisition scheme, called compressive CSI acquisition, which will obtain instantaneous CSI of only a subset of all the channel links and statistical CSI for the others, thus forming the mixed CSI at the BBU pool. This subset is determined by the statistical CSI. Then we propose a new stochastic beamforming framework to minimize the total transmit power while guaranteeing quality-of-service (QoS) requirements with the mixed CSI. Simulation results show that the proposed CSI acquisition scheme with stochastic beamforming can significantly reduce the CSI overhead while providing performance close to that with full CSI.