Aluminum alloys pose challenges to laser cutting due to their high thermal conductivity and reflectivity. Some of the shortcomings appearing during the laser cutting of aluminum alloys can be solved using a flexible, short−wavelength fiber laser. Previous research studies have focused their attention on the microfeatures of the cutting edge; however, the final impact of these features on the mechanical properties has not been thoroughly determined. This work investigates the effect of the processing parameters (laser power, cutting speed, and assist gas pressure) on the mechanical performance of AA2B06−T4 alloy sheets having 0.5 mm and 1 mm in thickness; the impact on the mechanical properties is explained in terms of the microfeatures produced in the cutting edge after laser cutting. It was observed that the striations formed on the cut edge have a significant influence on the final mechanical properties. An angle of the striations around 15−20°, obtained for a severance energy (SE) in the range of 6.67–13.34 J/mm2, was observed to give better mechanical properties. On the other hand, better surface roughness was observed for an assist gas pressure of 1.5 MPa. The width of the HAZ was reduced up to 20 μm using a standard cylindrical nozzle. Finally, it was observed that the fatigue strength of the samples exceeded the aeronautic requirements when the processing parameters were in the range mentioned above. These results demonstrate the capabilities of fiber laser cutting for aluminum alloys as a processing technique suitable for aeronautic applications.