In order to disintegrate nuclear fuel rods in the grid connection structure, a 10 kW fiber laser was used to cut a stainless steel simulation component with four layers of 3 mm thick plates and 12 mm gaps. The slit width is regarded as an important indicator to evaluate the cutting quality of the four-layer stainless steel plate. The results showed that good laser cutting quality can be successfully achieved under the proper process parameters. The widths of the cut seams of the four layers of grating after cutting were 1.25, 1.65, 1.80, and 1.92 mm. As the auxiliary gas pressure decreased layer by layer, the metal melting pool for the first two plates was mainly destroyed by the auxiliary gas. The cutting quality was good, and the slit area was mainly austenite with the presence of some ferrite. The third- and fourth-layer plates almost had no gas flow to assist blowing off, so the cut surface was an uneven melting pit, the cutting quality was poor, and the cut seam area ferrite content was higher than the upper plate cut seam area. At the same time, due to the lack of airflow cooling of the bottom plate, high laser energy, and long heating time, grain coarsening occurred, while grain deformation and a large number of dislocations existed. It can provide process support and technical guidance for the disintegration of nuclear fuel rods.