The specially-shaped Polycrystalline Diamond Compact (PDC) cutter is widely used in drill bit design due to its advantages of high rock cutting efficiency, strong impact resistance and long service life in hard and abrasive formation drilling. A detailed understanding of rock cutting behavior of worn specially-shaped PDC cutter is essential to improve the drilling efficiency and decrease the drilling costs. In this paper, the theoretical models of two new principles (loading performance (LP) and cutting performance (CP)) are derived for evaluating the cutting process of worn specially-shaped cutter, the theoretical models consider the factors, such as cutter geometry, aggressiveness, stress state, working life, and rock cutting efficiency. Besides, the numerical model of heterogeneous granite is developed using finite element method combined with Voronoi tessellation, the LP and CP of 12 kinds of worn specially-shaped PDC (SPDC) cutters are analyzed. The results found that the mechanical specific energy (MSE) of worn cutters first increase and then decrease with increasing the cutting depth, and the MSE increase with the increase of back rake angle except for Conical cutter and Wedge-shaped cutter. From the perspective of CP, the worn PDC cutters are more suitable for the smaller cutting depths, and the back rake angle has little effect on the CP of the specially-shaped worn PDC cutters. Conical cutter, Saddle-shaped cutter and Ellipse-shaped cutter have the highest CP value, while Rhombus-shaped cutter, Convex cutter and Wedge-shaped cutter have the lowest value in selecting cutters. This research leads to an enhanced understanding of rock-breaking mechanisms of worn SPDC cutters, and provides the basis to select of specially-shaped PDC cutters for the specific target formation.