Using two-dimensional magnetohydrodynamics (MHD) simulations, we investigate the dynamical properties of Type Ia supernova remnants (SNRs) evolved either in a uniform ambient medium or from an interaction with a dense clump. The initial conditions assume that the expansion of the supernova ejecta is of free inertia with a power-law density distribution in the outer part of the ejecta. To include the effects of the diffusive shock acceleration process and the escape of the accelerated particles from the shock front, we use different adiabatic indices in the simulations to study the dynamical evolution of the Type Ia SNRs. Moreover, we investigate the interactions of a SNR with either a small or a large clump. A double-shock structure with a contact discontinuity is produced as the ejecta flow supersonically in the ambient medium; Rayleigh–Taylor instability is clearly shown as fingers near the contact discontinuity in the contour maps of density, and a high density and a high magnetic field can be triggered because of the instability around the Rayleigh–Taylor fingers. We perform simulations with different adiabatic indices, and the results show that a narrower intershock region is produced with a smaller adiabatic index because a larger compression ratio for the SNR shock is induced. The influence of the Rayleigh–Taylor instability on the morphologies of both the forward and reverse shocks is more significant with a smaller adiabatic index. Finally, the simulations of a SNR interacting with a dense clump show that the morphology of the remnant is greatly twisted after the collision, and a filament with a high density and a high magnetic field can be produced as a SNR colliding with a large dense clump.