Nd∶TSAG magneto-optical crystal with the size of φ50 mm×100 mm were grown by Czochralski method for the first time. The structure, spectra, magneto-optical, and thermal properties of the crystal were studied in detail. Spectral parameters, such as oscillator strength, line strength, intensity parameter Ω_t, transition probability between ⁴F₃/2→⁴I_J energy levels, radiation lifetime, and fluorescence branching ratio were calculated. The doping concentration of Nd∶TSAG polycrystalline samples was optimized, and the best doping concentration of Nd³⁺(atomic fraction) is 1%. The results of X-ray diffraction analysis of crystal and powder show that the crystal has a pure phase and good crystal quality. The separation coefficient of Nd³⁺ in TSAG crystal is 0.64. In the visible and near infrared bands, the transmittance of Nd∶TSAG crystals is over 80%, except for the characteristic absorption of Tb³⁺ and Nd³⁺. With 808 nm excitation, the strongest fluorescence peak of Nd∶TSAG is around 1 070 nm. The refractive indices of Nd∶TSAG crystals at 473, 532, 632.8, and 1 064 nm are 1.925 9, 1.915 3, 1.903 8, and 1.885 2, respectively. The four-parameter Sellmeier refractive index equation is fitted. The Verdet constants of Nd∶TSAG measured by extinction method at 405, 532, 635, and 1 064 nm are 599.8, 202.8, 152.3, and 46.8 rad·m^-1·T^-1, respectively, which are higher than that of TGG crystals. At room temperature, the thermal conductivity of Nd∶TSAG crystals is 3.95 W/(m·K). The results show that Nd∶TSAG is an excellent magneto-optical crystal and a potential excellent laser crystal. Meanwhile, it is promising to realize the synergistic effect of magneto-optic and laser.