An exhaustive state-to-state dynamics study was performed to analyze the F + CHD3 -> FD(v ''j')+ CHD2(v) gas-phase abstraction reaction. Quasiclassical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories, were performed at different collision energies on an analytical potential energy surface (PES-2006) recently developed by our group. Whereas the CHD2 coproduct appears vibrationally and rotationally cold, most of the available energy appears as FD(v') product vibrational energy, peaking at v' = 2 and v' = 3, with the population in the latter level growing as the energy increases. The excitation function rises from the threshold of the reaction and then levels off at higher energies, with the maximum contribution from the FD(v' = 3) level. The state-specific FD(v') scattering distributions correlated with the coproduct CHD2 in the v(4) = 2 and v(3) = 1 states, at different collision energies, show a steady change from backward to forward scattering as the energy increases. This similar behavior for the two coproduct vibrational states, v(4) = 2 and v(3) = 1, agrees qualitatively with the experimental measurements. Comparison with theoretical and experimental results for the isotopic analogues, F + CH4 and F + CD4, shows that the title reaction presents a direct mechanism, similar to the perdeuterated reaction, but contrasts with that of the F + CH4 reaction. These results for the dynamics of different isotopic variants, always in qualitative and sometimes in quantitative agreement with experiment, show the capacity of the PES-2006 surface to correctly describe the title reaction, even though there are differences that could be due to deficiencies of the PES but also to the known limitations of the classical treatment in the QCT method.