In this paper, the effects of magnetic field and nonmagnetic Y³⁺ doping on spin state and spin reorientation in HoFeO₃ single crystal are systematically studied by the self-developed terahertz time-domain spectroscopy (THz-TDS) under magnetic field. By doping nonmagnetic Y³⁺, we find that the spin reorientation temperature range decreases. Meanwhile, we also find the type of spin reorientation of HoFeO₃ does not change with Y³⁺ doping, indicating that the Y³⁺ doping can exchange the interaction energy of Ho³⁺-Fe³⁺ without introducing any new magnetic structure. Moreover, the resonance frequency of quasi-ferromagnetic mode (q-FM) decreases with temperature increasing in the low temperature range, while the resonance frequency of quasi-antiferromagnetic mode (q-AFM) increases with temperature increasing in the high temperature range in Ho_1–xY_xFeO₃ single crystals. With the external magnetic field ( H _DC) applied along the (110) axis, on the one hand the magnetic field can not only tune the resonant frequency of q-FM but also induce the spin reorientation in Ho_1–xY_xFeO₃ single crystals, and on the other hand this magnetic field induced spin reorientation phenomenon can happen more easily if the temperature approaches to the intrinsic spin reorientation temperature range of the single crystals. Besides, the critical magnetic field induced spin reorientation increases with the doping of Y³⁺ increasing. Our research shows that THz spectroscopy data can be used to detect the doping concentration of Y³⁺ ions in HoFeO₃; in addition, Y³⁺ doping can make the spin state in HoFeO₃ crystal more stable and not easily affected by external magnetic fields. We anticipate that the role of doping and magnetic field in spin reorientation transition will trigger great interest in understanding the mechanism of the spin exchange interaction and the mechanism of external field tuning effect in the vast family of rare earth orthoferrites.