High power electronic chips are usually fabricated on about 50 µm thin Si wafers to improve heat dissipation. At these chip thicknesses mechanical dicing becomes challenging. Chippings may occur at the cutting edges, which reduce the mechanical stability of the die. Thermal load changes could then lead to sudden chip failure. Ultrashort pulsed lasers are a promising tool to improve the cutting quality, because thermal side effects can be reduced to a minimum. However, laser-induced periodic surface structures occur at the sidewalls and at the trench bottom during scribing. The goal of this study was to investigate the influence of these periodic structures on the backside breaking strength of the die. An ultrafast laser with a pulse duration of 380 fs and a wavelength of 1040 nm was used to cut a wafer into single chips. The pulse energy and the number of scans was varied. The cuts in the wafer were investigated using transmitted light microscopy, the sidewalls of the cut chips were investigated using scanning electron and confocal microscopy, and the breaking strength was evaluated using the 3-point bending test. The results indicated that periodic holes with a distance of about 20–30 µm were formed at the bottom of the trench, if the number of scans was set too low to completely cut the wafer; the wafer was only perforated. Mechanical breaking of the bridges caused 5 µm deep kerfs in the sidewall. These kerfs reduced the breaking strength at the backside of the chip to about 300 MPa. As the number of scans was increased, the bridges were ablated and the wafer was cut completely. Periodic structures were observed on the sidewall; the roughness was below 1 µm. The surface roughness remained on a constant level even when the number of scans was doubled. However, the periodic structures on the sidewall seemed to vanish and the probability to remove local flaws increases with the number of scans. As a consequence, the breaking strength was increased to about 700 MPa.