We use terahertz (THz) magnetic and electric fields to investigate the magnetic and optoelectronic responses of the Sm0.5Pr0.5FeO3(SPFO) crystal, respectively, by THz time-domain spectroscopy. It is found that the spin reorientation transition (SRT) in SPFO occurs in the temperature range of 175-210 K. The SRT is not observed in PrFeO3. The quasi-antiferromagnetic magnon frequency has a blue-shift from 0.42 THz (PrFeO3) to 0.46 THz (SPFO) at room temperature, due to the enhanced anisotropy constant. The refractive index of SPFO in the THz frequency decreases around 3% compared with that of the PrFeO3crystal. In addition, it can be found that the energy scale of crystal-field transitions has a red-shift for the doped single crystal. We expect our results to make rare-earth orthoferrites accessible to potential applications in THz spintronic devices.