A method for cutting a substrate by laser and a laser cutting device are disclosed. The method includes the following steps: engraving a plurality of intercrossed first parallel lines and second parallel lines on a substrate, in which regions for engraving a shape of sub-substrates are encircled between the first parallel lines and the second parallel lines; shaped lines are disposed in the regions; auxiliary split lines are engraved on an outside of the shaped lines; and a minimum distance from end portions of the auxiliary split lines towards the shaped lines to the shaped lines falls within the first default threshold. The method adopts the arrangement of the parallel lines and the auxiliary split lines to help splitting the substrate, and can increase stress rupture points in the process of cutting the substrate, avoid the phenomenon of rupture of the glass substrate in the cutting process, and effectively improve the yield of substrate cutting.