The state most certainly are empowered to deport illegal immigrants if the feds have failed in their constitutional duty per Art IV, Sec 4 of the Constitution to prevent invasion.
As confirmed by the Ninth and Tenth amendments, the states are constitutionally sovereign and it is their right AND duty to counter unconstitutional federal acts which by definition are acts of tyranny. That includes removing those illegally in their state.
Arizona asserted that, and lost. SCOTUS says immigration is solely the responsibility of the federal government.
I want to see it happen. Truly.