  We study the dynamics of homogeneous and isotropic
Friedmann-Lema\^itre-Robertson-Walker cosmological models with positive spatial
curvature in mimetic gravity theory, employing dynamical system techniques. Our
analysis yields phase space trajectories that describe physically relevant
solutions, capturing various stages of the cosmic evolution. Additionally, we
employ Bayesian statistical analysis to constraint the cosmological parameters
of the models, utilizing data from Supernovae Type Ia and the Hubble parameter
datasets. The observational datasets provide support for the viability of
mimetic gravity models, which effectively can describe the late-time
accelerated expansion of the universe.
