We discuss the dynamics of phase separation through the process of spinodal decomposition in a Fermi superfluid with population imbalance. We discuss this instability first in terms of a phenomenological Landau theory. Working within the mean-field description at zero temperature, we then find the spinodal region in the phase diagram of polarization versus interaction strength and the spectrum of unstable modes in this region. After a quench, the spinodal decomposition starts from the Sarma state, which is a minimum of the free energy with respect to the order parameter at fixed density and polarization and a maximum at fixed chemical potentials. The possibility of observing nontrivial domain structures in current experiments with trapped atomic gases is discussed.