The strong light-matter interaction in two dimensional (2D) materials portends an untapped potential for fiber lasers in the long sought-after terahertz to mid-infrared spectral range. Here, the broadband nonlinear optical properties of zero-gap 2D Ti2CTx MXene -- a class of 2D transition metal carbides that exhibit high laser damage threshold -- is discussed. Using the open aperture Z-scan method, for the first time the broadband saturable absorption properties of Ti2CTx in the 800-1560 nm spectral range are demonstrated. Specifically, it is shown that the high absorption and low saturation intensity of Ti2CTx make it an ideal saturable absorber for mode-locked fiber lasers operating at 1565 and 1051 nm, which exhibited pulse widths of 5.3 ps and 164 ps, respectively. Additionally, a Ti2CTx saturable absorber was used as a Q-switcher to realize a pulsed fiber laser operating at 2.8 µm, which showed excellent nonlinear absorption performance in the mid-infrared regime. This study significantly broadens the scope of materials available for non-linear optical applications in the near and mid-infrared regimes.