Laser processing of hard dielectric materials may include cutting a part from a hard dielectric material using a continuous wave laser operating in a quasi-continuous wave (QCW) mode to emit consecutive laser light pulses in a wavelength range of about 1060 nm to 1070 nm. Cutting using a QCW laser may be performed with a lower duty cycle (e.g., between about 1% and 15%) and in an inert gas atmosphere. Laser processing of hard dielectric materials may further include post-cut processing the cut edges of the part cut from the dielectric material, for example, by beveling and/or polishing the edges to reduce edge defects. The post-cut processing may be performed using a laser beam with different laser parameters than the beam used for cutting, for example, by using a shorter wavelength (e.g., 193 nm excimer laser) and/or a shorter pulse width (e.g., picosecond laser).