Methods and apparatus provide for: sourcing an ultra-thin glass sheet having first and second opposing major surfaces and perimeter edges therebetween, the glass sheet having a thickness between the first and second surfaces of less than about 400 microns; adhering at least one polymer layer directly or indirectly to at least one of the first and second surfaces of the glass sheet to form a laminated structure; and cutting the laminated structure using at least one of the following techniques: shear cutting, burst cutting, slit cutting, and crush cutting.