This article addresses the challenges encountered in underwater acoustic communication (UWAC) and presents a novel approach for chirp spread spectrum (CSS) communication. CSS is recognized for its ability to adjust to multipath and Doppler dispersion in underwater conditions, despite it usually demands a large bandwidth time product to achieve optimal performance. To address this constraint and improve data rate, the paper proposes a neural network-based receiver for spectral efficient M-ary CSS communication. M-ary communication is accomplished by transmitting chirps with different start and stop frequencies. At the receiver, a multilayer perceptron (MLP) artificial neural network and a one-dimensional convolutional neural network (1D CNN) are used for supervised classification. The neural network is trained offline using a comprehensive dataset developed by the BELLHOP ray tracing algorithm, which simulates various underwater acoustic channels. The application of VTRM pre-processing equalization aims to enhance performance. The simulation results illustrate the superior performance of the proposed receiver when compared to a conventional receiver based on a matched filter. The 16-ary chirp spread spectrum 1D CNN and MLP receivers show a gain of 6 and 4 dB, respectively, in a simulated channel after undergoing VTRM pre-processing. Furthermore, the utilization of a 16-ary 1D CNN receiver results in a noticeable 6 dB enhancement in two recorded channels. However, the MLP receiver outperforms the traditional receiver in terms of bit error rate. The article emphasizes the possibility of higher data rates and enhanced performance in underwater communication systems by employing the proposed M-ary CSS neural network-based method.