An electronic device is provided with a display such as a liquid crystal display. The display has a layer of liquid crystal material sandwiched between an upper display layer such as a color filter layer and a lower display layer such as a thin-film-transistor layer. An upper polarizer is formed on the upper surface of the color filter layer. A lower polarizer is formed on the lower surface of the thin-film-transistor layer. To protect display layers such as the color filter layer and the thin-film-transistor layer, a coating is deposited on a peripheral edge of the display layer. A laser is used to cut through portions of the polarizer that overhang the display layer while also cutting through the coating on the peripheral edge of the display layer. Following laser trimming operations, the coating is flush with an edge surface of the polarizer.