MXenes have attracted considerable interest for integrated nonlinear photonics owing to their broadband optical response and chemical tunability, yet investigations have focused predominantly on Ti-based compositions, leaving the nonlinear potential of double-transition-metal MXenes largely unexplored. Here we quantify the nonlinear optical response of the double-transition-metal MXene Mo2TiC2T_x and demonstrate its functionality as a waveguide-integrated nonlinear activation element for neuromorphic photonics. Z-scan measurements at 800nanometre reveal strong saturable absorption in films of two different thicknesses, yielding effective nonlinear absorption coefficients (βeff) between approximately -2.69×10³ and -0.88×10³ centimetrepergigawatt, with the nonlinear response decreasing at higher excitation intensities. The extracted nonlinear absorption is approximately one order of magnitude larger than that reported for Ti3C2T_x MXene under comparable conditions. We integrate an ultrathin Mo2TiC2T_x MXene layer onto a silicon rib waveguide to realize a compact nonlinear optical activation function, which, when implemented in a neural-network emulator, achieves 98.39% classification accuracy on the MNIST benchmark. This work expands the MXene material platform beyond Ti-based compositions and establishes double-transition-metal MXenes as promising candidates for high-performance integrated nonlinear photonic and neuromorphic computing technologies.