  We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, where
L\'evy processes are not necessarily comparable to $\alpha$-stable-like
processes. By assuming that the SDE has a unique solution, we obtain gradient
estimates of the associated semigroup when the drift term is locally H\"{o}lder
continuous, and we establish the ergodicity of the process both in the
$L^1$-Wasserstein distance and the total variation, when the coefficients are
dissipative for large distances. The proof is based on a new explicit Markov
coupling for SDEs driven by multiplicative pure jump L\'{e}vy noises, which is
derived for the first time in this paper.
