  In this paper, we study an initial boundary value problem of the
Cahn-Hilliard-Darcy system with a non-autonomous mass source term $S$ that
models tumor growth. We first prove the existence of global weak solutions as
well as the existence of unique local strong solutions in both 2D and 3D. Then
we investigate the qualitative behavior of solutions in details when the
spatial dimension is two. More precisely, we prove that the strong solution
exists globally and it defines a closed dynamical process. Then we establish
the existence of a minimal pullback attractor for translated bounded mass
source $S$. Finally, when $S$ is assumed to be asymptotically autonomous, we
demonstrate that any global weak/strong solution converges to a single steady
state as $t\to+\infty$. An estimate on the convergence rate is also given.
