This paper investigates the Orthogonal Time-Frequency Space (OTFS) Modulation for Underwater Mobile Acoustic Communications where the communication channel suffers from severe multipath and Doppler effects simultaneously. Practical OTFS modulation schemes with different parameters are designed for acoustic transmission at a center frequency of 115 kHz and a bandwidth of 11.5 kHz. The schemes are tested in lake experiments where the transmitter was anchored and the receiver was towed by a boat at a speed of approximately 1 m/s or 3.6 km/h. The receiver utilizes low-complexity channel estimation and equalization algorithms, such as NLMS (Normalized Least Mean Squares) and IPNLMS (improved proportionate NLMS) algorithms. The results show some insights of the OTFS scheme for acoustic communications. First, the mobile acoustic channel characteristics are different in the 2D delay-Doppler domain than those in the 1D time and frequency domains for the Single-Carrier Coherent Modulation (SCCM) and the Orthogonal frequency division modulation (OFDM), respectively. Second, in mobile scenarios, the OTFS scheme receiver effectively and significantly reduces the accuracy requirements of the Doppler compensation algorithm and provides better frequency-selective fading suppression and Doppler effect robustness compared to SCCM and OFDM schemes. Third, the OTFS scheme has better anti-multipath performance and reduces multipath interference by effectively differentiating signals on different paths in the 2D delay-Doppler domain.