In laser cleaving of brittle materials using the controlled fracture technique, thermal stresses are used to induce a single crack and the material is separated along the cutting path by extending the crack. One of the problems in laser cutting of glass with the controlled fracture technique is the cut deviation at the leading and the trailing edges of the glass sheet. This work is about minimizing this deviation through an optimization process, which includes laser beam geometry. It has been established that the thermal stresses generated during laser scanning are strongly dependent upon laser beam geometry. Experimental techniques are used to quantify cut deviation for soda-lime glass sheets under a set of conditions while finite element modeling is used to optimize the process and reduce (or eliminate) cut deviation. The experimental results of the effect of different laser beam geometries on cut path deviation have been presented in this study, along with the finite element modeling of the cutting process to simulate the transient effects of the moving beam and predict thermal fields and stress distribution. These predictions are compared with the experimental data. In comparison to other beam geometries, the triangular-forward beam at the leading edge and triangular-reverse and circular beam geometry at the trailing edge produces lower tensile stresses and hence minimizes the cut path deviation. The work also shows that beam divergence inside the glass plays a significant role in changing the cut path deviation at the bottom leading and trailing edges of the glass.