The wavelength-related optical nonlinearities of few-layer Mg-MOF-74 nanosheets were investigated in the wavelength region around 1.08, 1.94, and 2.85 μm by the closed aperture Z-scan, open aperture Z-scan and I-scan method. Under the excitation of 100-μJ laser pulses, the nonlinear refractive index (n2) of -7.7 ± 2.6, -131 ± 5 and 4.9 ± 0.2 cm2/W were obtained, respectively. The wavelength-related optical nonlinearity of the Mg-MOF-74 nanosheet was also investigated. In 2.85 μm wavelength region, the Mg-MOF-74 nanosheets shows a stable saturable absorption property with a modulation depth of 8% and a saturation intensity of 170 mJ/cm2. In the 1.08 and 1.94 μm wavelength regions, we can observe that the Mg-MOF-74 transits from saturable absorption regime to reverse saturable absorption regime with the increasing incident laser intensity. Employed as a saturable absorber in a Er:Lu2O3 laser, Mg-MOF-74 nanosheet shows a thickness-related laser modulation performance. The shortest laser pulse of 284-ns was achieved under a repetition rate of 116 kHz with a 6-nm-thick Mg-MOF-74 nanosheet, which corresponds to a pulse energy of 3.2 µJ and a peak power of 11.4 W.