He doesn't actually want them gone. He wants them oppressed and desperate.
That's actually been the standard Republican strategy for as long as I can remember, because they're trying to serve two purposes at the same time. On the one hand they want to appeal to the racists in their party, but on the other hand, they want to ensure that American businesses enjoy uninterrupted access to cheap and desperate labor. And the two actually complement each other pretty well. They can and do foment hatred and promise mass deportations and all of that to appeal to the racists, but never quite manage to actually solve the supposed problem, or even really make any headway on it, which means that businesses can stil take advantage of cheap and desperate labor and there are still "illegals" for the racists to rail against.
At this point, the most determined and successful opponent of progressivism in the US is the Democrat party.