We study Newton polytopes for cluster variables in cluster algebras $\mathcal{A}(Σ)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster variable can be written as a Laurent polynomial in the cluster variables of the initial seed $Σ$. The cluster variable Newton polytopes are the Newton polytopes of these Laurent polynomials. We show that if $Σ$ has principal coefficients or boundary frozen variables, then all cluster variable Newton polytopes are saturated. We also characterize when these Newton polytopes are \emph{empty}; that is, when they have no non-vertex lattice points.