This paper examines the single-fiber composite (SFC) test as a micromechanical method to evaluate the interfacial properties and fiber fracture mechanisms in fiber-reinforced composites. A micromechanical model is developed based on finite element analysis combined with cohesive element method to characterize the fiber fragmentation in relation to the matrix failure and interfacial debonding around a fiber break, as typical micro-scale damage observed in the SFC specimen. The analysis clarifies the damage evolution mechanism after the fiber fragmentation in carbon-fiber/epoxy composite system. Interfacial debonding influences significantly on the axial stress recovery from the fiber breaking point, which is a key factor for the subsequent fiber fragmentation. Moreover, it is found that the debonding growth is greatly affected by the matrix inelastic deformation or matrix crack. The simulated results are also discussed by comparison with other theoretical models or some experimental observations.