We present a numerical investigation of the bound-state pulse formation mechanism and evolutionary dynamics based on the pump strength and spectral filtering bandwidth in the all-fiber Mamyshev oscillator. Through the numerical simulation and analysis, the different mode-locked pulses’ (such as single pulses, bound-state pulses, and chaotic multi-pulses) regime transformation conditions are quantified. The results suggest that with an increase in the pump strength, the sub-pulse energy and output coupler of the Mamyshev oscillator show an inverse proportion trend, which plays an important role in increasing the number of sub-pulses in the bound-state pulses’ state. Furthermore, optimization schemes, such as adjusting the filter bandwidth and slowing down the accumulation of nonlinear effects, are proposed to achieve a high-energy pulse output in the Mamyshev oscillator.