An internal feature can be laser machined in strengthened glass sheets or panels by first laser machining a first scribe in a first surface proximate to the internal feature to be laser machined. The internal feature can be then laser machined by positioning a beam waist of a laser beam proximate to an opposite second surface by focusing the laser beam through the strengthened glass panel from the first surface. The internal feature is laser machined by repositioning the beam waist from the second surface to the first surface while removing material from a kerf surrounding the internal feature. When the laser beam waist is finally positioned proximate to the first surface material, the internal shape formed by the laser machining is easily and cleanly removed from the surrounding glass.