Defund it.
The challenge with that is that most of the Citizenship and Immigration Service’s operations are funded by fee for service. Unlike most of the rest of the government, their default setting is “on” (so long as the money from immigrants keeps flowing in), and since they aren’t funded by appropriated money, they don’t shut down.
The only way to shut them down would be a piece of legislation ordering them to do so. But it would need enough votes to override the expected veto.