In underwater acoustic (UWA) random access communication networks with multiple users and data packet transmissions, the packet collisions are the main cause of the network performance degradation. The aim of this paper is to investigate interference cancellation (IC) techniques capable of resolving such collisions in a low-complexity modem with single-carrier modulation and single transducer. More specifically, in this modem, the IC is used at multiple stages of the receiver. Firstly, the IC is performed for cancelling the multipath interference to improve the equalization performance in comparison with the linear equalization and Rake combining. Secondly, the IC removes the interference from collided data packets within extracted signal segments after identifying the collisions. Finally, the IC is applied to the received baseband signal to improve the data packet detection. The modem performance is investigated in a lake experiment with intensive multipath channels. The experimental results demonstrate high detection performance of the proposed modem design and show that the proposed IC techniques can significantly improve the throughput of random access UWA networks.