Sensing will be an important service of future wireless networks to assist innovative applications such as autonomous driving and environment monitoring. Perceptive mobile networks (PMNs) were proposed to add sensing capability to current cellular networks. Different from traditional radar, the cellular structure of PMNs offers multiple perspectives to sense the same target, but the inherent interference between sensing and communication along with the joint processing among distributed sensing nodes (SNs) also cause big challenges for the design of PMNs. In this paper, we first propose a two-stage protocol to tackle the interference between two sub-systems. Specifically, the echoes created by communication signals, i.e., interference for sensing, are first estimated in the clutter estimation (CE) stage and then utilized for interference management in the target sensing (TS) stage. A networked sensing detector is then derived to exploit the perspectives provided by multiple SNs for sensing the same target. The macro-diversity from multiple SNs together with the array gain and the higher angular resolution from multiple receive antennas of each SN are investigated to reveal the benefit of networked sensing. Furthermore, we derive the sufficient condition to guarantee one SN's contribution is positive, based on which a SN selection algorithm is proposed. To reduce the communication workload, we propose a distributed model-driven deep-learning algorithm that utilizes partially-sampled data for CE. Simulation results confirm the benefits of networked sensing and validate the higher efficiency of the proposed CE algorithm than existing methods.