The reflecting Schmidt plate of the Large sky Area Multi-Object Spectroscopic Telescope (LAMOST) is segmented with 24 thin hexagonal sub-mirrors of 1.1 meters tip-tip each. It not only serves as active corrector for eliminating spherical aberration of the fixed segmented spherical primary mirror but also collaborates with focal plane in between to do pointing and tracking with an alt-azimuth mounting. This paper describes the evolution and evaluation of the structural design of the reflecting Schmidt mirror cell onto which sub-mirror systems are connected. Technical requirements are presented before a brief history of evolution of the mirror cell throughout the progress of the LAMOST project. Based on final elevation driving and balancing scheme, a final design of the mirror cell has been reached and evaluated with finite element method. Following the principle of deflection-independent, the design is actually a hybrid of space frame and truss structure meeting technical requirements with low weight, high stiffness and clear accessibility. Gravitational analysis results that the maximum deflection is about 1 mm through overall observing sky area of -10º≤δ≤90º, and modal extraction finds that the lowest eigenfrequency is about 30 Hz. Relevant investigation of elevation axis trunnion preload and driving force effect as well as evaluation of typical thermal and static wind disturbance also confirm the excellent performance of the final design of the Schmidt mirror cell.