The assessment of surgical skill is crucial for indicating a surgeon's proficiency. While motion analysis of surgical tools is widely used in endoscopic surgery, it is not commonly applied to open surgery. Instead, open surgery skill assessment relies on observing the trajectory of surgical tools on tissue. This observation-based method often lacks clear standards, leading to inaccurate assessments. This paper presents a method for evaluating cutting skill in open surgery through scalpel motion analysis. A 3D multiple-facet ArUco code cube is designed, and a dataset of tip coordinate system poses for various scalpels in the ArUco code coordinate system (ACS) is established using the pivot calibration method. The YOLOv8 model and an image dataset of different scalpels are used to identify the scalpel type and select its tip position. The tip position is then transformed from ACS to a binocular camera coordinate system (BCS), representing the incision curve made by the scalpel. Five assessment metrics are proposed to quantify the surgeon's cutting skill: average incision curvature deviation, incision length difference, incision endpoint deviation, average incision deviation, and average cutting jerk. Experiments involving twenty expert and novice surgeons performing four common incisions (straight line, polyline, semicircle, and cross line) demonstrate the metrics' effectiveness. The metrics provide a clear, objective display of individual cutting skills, and a combined ranking reveals comparative skill levels. This study offers a precise method for evaluating surgeons' cutting skills with a scalpel in open surgery.