Self-pulsing instability in the ytterbium-doped fiber (YDF) laser is investigated with the pump-bypassed cavity configuration. The residual pump light acts as a probe of the intracavity dynamics, and the temporal behavior of the light shows correlations with the self-mode locking instability in the original cavity and the sustained self-pulsing instability in the modified cavity of the YDF laser. The results suggest that the interactions among stimulated emission, pump absorption and/or reabsorption could account for self-pulsing instability in the YDF laser. The pump-bypassed laser cavity configuration can be used to investigate the instabilities of various kinds of fiber lasers.