Chemically strengthened glass is widely used in electronic device display screens; however, they are difficult to cut. With the high peak power of a picosecond laser and long focal depth of a Bessel beam, a narrow-modified plane is machined inside the chemical glass. Owing to its original stress and stress induced by the picosecond laser, chemically strengthened glass accurately self-breaks along the modified plane with cutting speed of 400 mm/s and surface roughness of 395 nm. Experimental results show that pulse energy and pulse modification spacing are the main parameters affecting cutting speed and quality.