In this work, the optical parameters of a 550 μm thick deuterated triglycine sulfate (DTGS) crystal in the range of 0.3–1.5 THz were investigated in low and high fields by time-domain spectroscopy. The X and Z axes of the refractive index ellipsoid were identified, and the refractive indices and extinction coefficients were determined. In addition, it was shown that, in strong THz fields, a phonon A-mode with a frequency of about 40 cm−1 can be excited in the DTGS crystal when the THz wave vector coincides with the polar axis of the crystal and the polarization of the THz radiation coincides with the X-axis of the crystal. The use of the observed effect and the determination of the mode excitation parameters can be twofold. First, they show the limits of the THz field for non-invasive action on the crystal. Second, they present the mode excitation conditions that can be used, for example, in controllable absorbers.