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The Hawking evaporation process has important implications for our understanding of the universe, as it suggests that black holes are not eternal and can eventually evaporate away completely. We evaluate the Hawking evaporation process of AdS Schwarzschild scalar-tensor-vector gravity black hole by using Stefan-Boltzmann law and find out that Hawking evaporation rate depends on the AdS radius land deviation parameter αof the scalar-tensor-vector gravity. We analyze that for small values of AdS radius land positive deviation parameter αblack hole evaporates quickly. While there is exponential increase in lifetime of the black hole for large AdS radius land negative deviation parameter α. Moreover, we find out thermodynamical quantities like Helmholtz free energy, internal energy, pressure, enthalpy, Gibbs free energy and specific heat and show that how deviation parameter αand the correction parameter ζof the first order corrected entropy play vital role on the stability and phase transitions of the black holes.