The process of permeation damage of the filling medium in the fracture is critical to the stability of the fractured rock mass. This study focused on the seepage failure process of filling materials in fractures and faults. To investigate the effects of axial stress and clay content, a series of experimental tests were conducted on internally unstable granular soil specimens with different clay contents under different axial stresses. The variations of flow rate and hydraulic conductivity were recorded and analyzed during the tests, and the typical process of seepage failure was summarized. The flow rate, hydraulic conductivity, and their growth rates were found to be smaller under high axial stress compared to low axial stress, and the flow rate of samples with higher clay content was smaller than those with lower clay content. Initially, the hydraulic conductivity decreased slightly due to clay and fine particle rearrangement, and remained nearly constant when the hydraulic gradient was small. However, as the hydraulic gradient increased, the hydraulic conductivity began to increase in response to the loss of clay and fine particles.