With the popularization of autonomous vehicle (AV) technology, mixed traffic flows that consist of AVs and human-driven vehicles (HDVs) will appear in the real world. Although many studies of the features of mixed traffic flow have been carefully evaluated, few studies have focused on the effect of aggressive driving performance on mixed traffic flow. This study aims to develop an approach to evaluate the effects of aggressive driving on the stability and capacity performance under the conditions of AV and HDV mixed traffic flow. First, since a car-following model can describe the relationship between vehicles, we calibrate a car-following model for aggressive driving and nonaggressive driving behaviors based on real traffic data and previous research results. Then, in a mixed traffic flow environment, a basic linear stability formula and capacity calculation expression are developed that consider the effects of vehicle order on the capacity. Finally, because the proportion of aggressive driving and aggressive driving parameters may change, nine combinations of three aggressive driving proportions and three driving parameter cases are used for the sensitivity analysis. The results indicate that the effect of aggressive driving on mixed traffic flow is complex. When the proportion of aggressive driving is less than 35%, the increase in the proportion of aggressive driving increases the traffic capacity and reduces the unstable part. However, when the proportion of aggressive driving is greater than 35%, the increase in the proportion of aggressive driving increases the unstable part. When the penetration rate of AVs exceeds 0.490, mixed traffic flow remains stable at all aggressive driving proportions. In addition, the capacity of a mixed traffic flow may be improved as the penetration rate of AVs increases. To a certain extent, these conclusions provide a theoretical basis for formulating different management modes of AVs and HDVs.