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The goal of this work is to develop a phase-field fracture model capable of capturing mixed- mode fracture propagation behavior. In nature, failure of rocks and rock-like materials is usually accompanied by the propagation of mixed-mode fractures. To address this problem, some recent studies have incorporated mixed-mode fracture propagation criteria to the classic phase-field frac- ture model and proposed new energy splitting methods to split the total crack driving energy into mode-I and mode-II parts. But these new models have sometimes the shortcomings of being not numerically-robust or not physically sound. From a numerical viewpoint, they are all solved with staggered solution schemes. In this work, an existing energy splitting method for masonry-like materials is modified and incorporated into the phase-field model for mixed-mode fractures. A fully-monolithic scheme is used to solve the model. Therein, a primal-dual active set method is employed for treating the fracture irreversibility. Moreover, our computational framework uses adaptive mesh refinement of a predictor-corrector type and parallel computing to reduce the com- putation time. Three numerical tests are carried out, and the results of the new model are compared to those of existing models, demonstrating the numerical robustness and physical soundness of the new model. In total, six splitting methods are compared and computationally analyzed.