In this paper the possibility to optimize the glass dicing process by controlling the axicon-generated Bessel beam ellipticity is presented. Single-shot intra-volume modifications in soda-lime glass followed by dicing experiments of 1 mm-thick samples are performed. The Bessel beam ellipticity is essential for glass dicing process. Such beam generates intra-volume modifications with transverse crack propagation in dominant direction. Orientation of these modifications parallel to the dicing direction gives significant advantages in terms of processing speed, glass breaking force and cutting quality.