PDC (polycrystalline diamond compact) drill bits are widely employed for rock-breaking in many industries like underground engineering and building constructions. The cutter layout would directly affect the overall performance of the drill bits. Field applications show that the staggered cutter layout strategy of dual-cutter can increase the drilling efficiency of the PDC bit. In order to explore the rock breaking mechanism of this type of drill bit, a numerical model of a dual-cutter and rock breaking with damage evolution based on a hybrid finite and cohesive element method (FCEM) has been established in this work. The model is verified through Brazilian disk tests. The rock breaking processes of this type of bit have been analyzed, including crack initiation, propagation, and the formation of rock debris. Moreover, the effects of horizontal and vertical offset of the back cutter on the MSE (mechanical special energy) have been investigated. Results demonstrate that the dual-cutter can prominently reduce the MSE compared to a single-cutter. The vertical offset of the back cutter has a minor effect on the MSE, while the horizontal offset is of great significance on the MSE. On this basis, the relationships between the MSE and both the vertical and horizontal offset coefficients have been built based on the response surface methodology (RSM). Finally, an optimized layout solution, with optimal vertical and horizontal offset coefficients of 0.641 and 0.497, is determined via the Gray Wolf algorithm.