To investigate the effects of different aggregate mixing schemes on the mechanical properties of concrete, this study proposes a method that can rapidly build a two-dimensional random aggregate model of mixed aggregate concrete. First, a deformed ellipse is used to represent the pebbles, and a method that can generate a model of the crushed stone with sharp edges is proposed. Second, a point cloud with state functions is constructed in the specimen space to improve the efficiency of aggregate placement. Third, the action scope and mathematical methods are combined to enable fast intrusion judgments between aggregates. Fourth, the aggregates are graded and classified according to the proportion of different types of aggregates in each level, which is controlled using the critical domain. Finally, simulations of crack propagation are performed on the specimens generated using three different aggregate mixing schemes. The simulation results show that the shape of the concrete aggregates and the proportion of different types of aggregates affect their mechanical properties, which is consistent with the findings of previous studies. The effectiveness of the modeling approach is verified by comparing the modeling efficiency analysis and simulation results.