Seepage-induced failure may disable the bearing capacity of foundations in dams and embankments. However, the evolution mechanism of the seepage failure process in granular soils is not well understood. In this paper, a series of laboratory hydraulic tests were performed to investigate the seepage failure process in sandy gravels and fine-grained sands. Seepage behaviors of the hydraulic gradient, seepage flow velocity, and permeability coefficient were observed, and then, the Reynolds number was obtained to describe the seepage regime. By linking the hydraulic gradients with the Reynolds number, the seepage failure process was quantitatively divided into four phases: (i) incubation ( Re < 0.85 ), (ii) formation ( 0.85 ≤ Re ≤ 5 ), (iii) evolution ( 5 < Re ≤ 50 ), and (iv) destruction ( 50 < Re ). The findings of the study identified an approximately linear relationship between the hydraulic gradient and the seepage velocity in the phases of incubation and formation in which the viscous drag effects are not negligible, corroborating Darcy’s view. However, in the phases of evolution and destruction, the hydraulic gradient and the seepage velocity are nonlinearly related, indicating that the inertial force plays a leading role, and the quadratic equation is relevant for the regime transition from laminar flow to turbulent flow. Finally, the mechanism of each phase in the seepage failure process was clarified. Fine content and uniformity coefficient are internal factors that affect the potential of seepage failure, while the seepage force that drives the transport of fine particles is an underlying cause that promotes the development of seepage failure. This study will be quite useful in identifying the limits of applicability of the well-known “Darcy’s law,” in further improving the physical modelling associated with fluid flow through granular soils.