MXenes comprise a new class of 2D transition metal carbides, nitrides, and carbonitrides that exhibit unique light-matter interactions. Recently, 2D Ti3CNTx (Tx represents functional groups such as -OH and -F) was found to exhibit nonlinear saturable absorption (SA) or increased transmittance at higher light fluences, which is useful for mode locking in fiber-based femtosecond lasers. However, the fundamental origin and thickness dependence of SA behavior in MXenes remain to be understood. 2D Ti3CNTx thin films of different thicknesses are fabricated using an interfacial film formation technique to systematically study their nonlinear optical properties. Using the open aperture Z-scan method, it is found that the SA behavior in Ti3CNTx MXene arises from plasmon-induced increase in the ground state absorption at photon energies above the threshold for free carrier oscillations. The saturation fluence and modulation depth of Ti3CNTx MXene is observed to be dependent on the film thickness. Unlike other 2D materials, Ti3CNTx is found to show higher threshold for light-induced damage with up to 50% increase in nonlinear transmittance. Lastly, building on the SA behavior of Ti3CNTx MXenes, a Ti3CNTx MXene-based photonic diode that breaks time-reversal symmetry to achieve nonreciprocal transmission of nanosecond laser pulses is demonstrated.