The separation of complex inner and outer contours of glass articles with curved surfaces using ultrashort pulsed lasers is reported. Single-pass, full-thickness modifications along the entire substrate are achieved using a processing optics that allows for beam shaping of non-diffracting beams and, additionally, for aberration compensation of phase distortions occurring at the curved interface. The glass articles finally separated by thermal stress or via selective etching meet the demands of the medical industry in terms of micro-debris, surface quality, and processing speed.