In this brief we present a design of a full-duplex (FD) underwater acoustic communication (UAC) receiver with a two-sensor transducer. The transducer consists of two piezoceramic cylinders cast together in polyurethane resin; one acts as a hydrophone and the other a projector. As the distance between the projector and hydrophone is extremely short, a high level of self-interference (SI) from the projector is received at the hydrophone. This SI must be eliminated to enable farend data demodulation. In this work, we adopt a digital SI cancellation scheme based on adaptive filtering. We investigate the SI cancellation and far-end data demodulation performance with the two-sensor transducer in tank and lake experiments. The Rake receiver is used for the far-end data demodulation. As demonstrated by the experimental results, the far-end SNR loss in the FD experiment is less than 3 dB compared to the half-duplex experiment when there is only far-end transmission.