In applications such as material detection and imaging, terahertz radiation sources with high repetition rates can significantly shorten the sample inspection time and terahertz sources with a broad tuning range can effectively enrich spectroscopic information and expand the range of detectable materials. To address the difficulty in simultaneously achieving high repetition rate, wide tuning range, and high output power in existing terahertz sources, this work theoretically and experimentally investigates the output characteristics and underlying physical mechanisms of a high-repetition-rate, broadly tunable terahertz parametric oscillator (TPO) based on an MgO:LN crystal.First, starting from the stimulated polariton scattering (SPS) process, a net-gain model for the terahertz parametric process is established to systematically analyze the effects of pump peak power density, pump beam size, and crystal absorption on the terahertz generation efficiency and tuning range. The theoretical results show that appropriately increasing the pump energy density can enhance the terahertz parametric gain and effectively extend the tuning capability toward the high-frequency side. Experimentally, a high-repetition-rate electro-optically Q-switched 1064 nm laser is used as the pump source to construct the MgO:LN-based TPO. By optimizing the phase-matching angle and the pump beam size, continuous terahertz-wave output is achieved with a repetition rate of 4 kHz and a frequency tuning range of 1.05-4.96 THz. The experimental results are in good agreement with the theoretical analysis. When the pump power is 28 W, a maximum average output power of 120 μW is obtained at 1.7 THz, corresponding to an energy conversion efficiency of 4.3×10^-6 and an estimated peak power of about 10.3 W. Further analysis indicates that in the high-frequency terahertz region, a higher pump peak power density helps overcome the losses caused by crystal absorption, thereby improving the output power and broadening the accessible tuning range.