The multiple-input multiple-output (MIMO) architecture with the layered space-time codes is a very promising solution for the high data rate underwater acoustic communications. The realization of this potential advantage, however, needs the essential layered space-time signal processing methods for canceling the interference resulting from the multipath propagation and the asynchronous arrivals of the sub-streams due to the different propagation delays, and the interference between the transmitted streams superposed in each receiving hydrophone. In this paper, the low-complex layered space-time signal detection scheme for the underwater acoustic communications is investigated. A propagation delay-based ordered successive interference cancellation (OSIC) algorithm is proposed at first. Sub-streams are sorted at the receiver according to the arrival orders resulting from the relative propagation delays inherent in the underwater acoustic channels from the transmitting transducers to the receiving hydrophones. The sub-stream with the first arrival is detected first. The proposed OSIC algorithm based on the "first-come first-go" principle has an advantage in the reduction of the interference from yet-to-be-detected sub-streams, therefore improving the detection performance at each step. The analysis manifests that the delay-based ordering is an optimal detection ordering to minimize the probability of overall block error for the asynchronous space multiplexing architectures. Then the ordering procedure is given which is performed by estimating the relative delays between the MIMO channels and requires only one ordering before the signal detection. This channel estimation-based method simplifies dramatically the ordering procedure and the calculations, therefore reducing substantially the calculation complexity of the layered signal detection. Finally, the single-carrier frequency domain equalization is employed to compensate for the multipath interference and the asynchronous arrival interference from the underwater acoustic propagation. Numerical results show that the performance gain can be obtained with the delay-based OSIC detection algorithm relative to the detection without ordering; moreover the gain increases substantially with the data rate. The investigation results demonstrates, on the other hand, that the inherent relative propagation delay in the underwater acoustic channels leading to asynchronous interference to the signal detection can be turned into an advantage to improve the performance with the efficient space-time signal processing algorithms.