As a classic auxiliary line construction approach, the segment cutting and extension method is widely adopted in geometric reasoning to convert problems about the quantitative relation of discrete line segments into proof tasks of congruent figures. This paper discusses the inherent logical rules of this method, sorts out its general thinking workflow, and proposes a taxonomy of transformation strategies indexed by the geometric transformation that the construction performs rather than by the appearance of the figure. Beyond the simple classification of problem types, this study further explores the cognitive barriers that learners usually encounter when applying the method, and compares this approach with other common auxiliary line techniques in geometric reasoning. Different from many existing discussions which only focus on case demonstration, this paper emphasizes the logical essence of geometric transformation rather than routine problem-solving skills. It also analyzes how this method reflects the core idea of the axiomatic geometry system, and provides corresponding suggestions for geometric reasoning guidance. The analysis shows that the value of segment cutting and extension lies not only in proving equal or multiple relations of line segments, but also in training learners to establish flexible association among angles, sides and graphic structures. This research can offer reference for the design of geometric reasoning activities and the exploration of transformation-oriented geometric thinking.