Deportation:  Take him  — or stay out.
The nonsense about a country refusing to take back an alien criminal can be stopped with enforcement of a law on the books already.
“On being notified by the [DHS Secretary] that the government of a foreign country denies or unreasonably delays accepting an alien who is a citizen, subject, national, or resident of that country after the [DHS Secretary] asks whether the government will accept the alien under this section, the Secretary of State shall order consular officers in that foreign country to discontinue granting immigrant visas or nonimmigrant visas, or both, to citizens, subjects, nationals, and residents of that country until the [DHS Secretary] notifies the Secretary that the country has accepted the alien.”
8 U.S.C. Section 1253(d)