The relaxor ferroelectric single crystal (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3(PMN-PT) has high piezoelectric constants, and thus has a good application prospect in the field of highly sensitive piezoelectric sensors. In this paper, for relaxor ferroelectric single crystal PMN-PT, the bulk acoustic wave characteristics on pure- and pseudo-lateral-field-excitation (pure- and pseudo-LFE) modes are investigated. LFE piezoelectric coupling coefficients and acoustic wave phase velocities for PMN-PT crystals in different cuts and electric field directions are calculated. On this basis, the optimal cuts of pure-LFE and pseudo-LFE modes of relaxor ferroelectric single crystal PMN-PT are obtained, namely, (zxt)45° and (zxtl)90°/90°, respectively. Finally, finite element simulations are carried out to verify the cuts of pure-LFE and pseudo-LFE modes. The simulation results show that the PMN-PT acoustic wave devices in pure-LFE mode have good energy-trapping effects. For PMN-PT acoustic wave devices in pseudo-LFE mode, when the device is in air, no obvious energy-trapping emerges; when the water (as a virtual electrode) is added to the surface of the crystal plate, an obvious resonance peak and the energy-trapping effect appears. Therefore, the PMN-PT pure-LFE device is suitable for gas-phase detections. While the PMN-PT pseudo-LFE device is suitable for liquid-phase detections. The above results verify the correctness of the cuts of the two modes. The research results provide an important basis for the development of highly sensitive LFE piezoelectric sensors based on relaxor ferroelectric single crystal PMN-PT.