This letter studies a cellular-connected unmanned aerial vehicle (UAV) scenario, in which a UAV user communicates with ground base stations (GBSs) in cellular uplink by sharing the spectrum with ground users (GUs). To deal with the severe air-to-ground (A2G) co-channel interference, we consider an adaptive interference cancellation (IC) approach, in which each GBS can decode the GU's messages by adaptively switching between the modes of IC (i.e., precanceling the UAV's resultant interference) and treating interference as noise (TIN). By designing the GBSs' decoding modes, jointly with the wireless resource allocation and the UAV's trajectory control, we maximize the UAV's data-rate throughput over a finite mission period, while ensuring the minimum data-rate requirements at individual GUs. We propose an efficient algorithm to solve the throughput maximization problem by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that our proposed design significantly improves the UAV's throughput as compared to the benchmark schemes without the adaptive IC and/or trajectory optimization.