During laser cleaving of brittle materials, with the controlled fracture technique, thermal stresses are generated which induce the crack and extend it along the cutting path subsequently causing material separation. One of the problems in laser cutting of glass with this technique is the cut path deviation at the leading and the trailing edges of the glass sheet. Previous work with a continuous beam diode laser has shown the deviation to be partly due the high magnitudes of thermal stresses generated near the edges of the sheet. This paper reports on the effects of using a pulsed diode laser to cut soda lime glass. The effect of pulse parameters and cutting speed on the quality output variables such as cut deviation angle and surface finish are studied. Finite element modelling is also used to simulate the effects of the moving beam on stress generations to facilitate the understanding of the process mechanisms and the results are compared with the experimental data. This work shows how to minimise the cut path deviation at the edges by reducing thermal stresses using optimum pulsed diode laser parameters and providing additional flexibility to the process.