The dynamic performance of differential Symmetric Mach Zehnder Interferometer (SMZI) switch based on semiconductor optical amplifier (SOA) phase shifter is analyzed. For the first time, we investigate the effect of two photon absorption (TPA) as a nonlinear effect of SOA on the push-pull MZ switching scheme where SOAs are placed in each arm. It is shown that our switch is easily affected by TPA phenomena in SOA-SMZI. We use finite difference beam propagation (FD-BPM) method for analysis and solve nonlinear modified Schrödinger equation. In our results we take into account all nonlinear effects relevant to subpicosecond regime in SOA such as group velocity dispersion (GVD), Kerr effect, carrier heating and spectral hole burning (SHB).