In this paper, the effects of magnetic field and nonmagnetic Y ³⁺doping on spin state and spin reorientation in HoFeO ₃single crystal are systematically studied by the self-developed terahertz time-domain spectroscopy (THz-TDS) under magnetic field. By doping nonmagnetic Y ³⁺, we find that the spin reorientation temperature range decreases. Meanwhile, we also find the type of spin reorientation of HoFeO ₃does not change with Y ³⁺doping, indicating that the Y ³⁺doping can exchange the interaction energy of Ho ³⁺-Fe ³⁺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 _xFeO ₃single 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 _xFeO ₃single 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 Y ³⁺increasing. Our research shows that THz spectroscopy data can be used to detect the doping concentration of Y ³⁺ions in HoFeO ₃; in addition, Y ³⁺doping can make the spin state in HoFeO ₃crystal 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.