  We revisit the two-field mimetic gravity model with shift symmetries recently
proposed in the literature, especially the problems of degrees of freedom and
stabilities. We first study the model at the linear cosmological perturbation
level by quadratic Lagrangian and Hamiltonian formulations. We show that there
are actually two (instead of one) scalar degrees of freedom in this model in
addition to two tensor modes. We then push on the study to the full non-linear
level in terms of the Hamiltonian analysis, and confirm our result from the
linear perturbation theory. We also consider the case where the kinetic terms
of the two mimetic scalar fields have opposite signs in the constraint
equation. We point out that in this case the model always suffers from the
ghost instability problem.
