I arrived from Mexico by hiding. I don’t have any papers to be in the United States. I traveled with other people like me. If immigration catches me and I don’t say I’m from Mexico, can they still deport me?
Before U.S. immigration officers can try to deport (or “remove”) you from the U.S., they must first prove that you are a foreigner (or, as lawyers would say, they must prove your “alienage”) and second, they must prove that you are present in the U.S. without authorization.
The immigration authorities have different ways of doing these things, but probably the easiest one is for you to volunteer the information. However, you cannot be legally forced to tell immigration officers anything. In fact, staying silent when they ask you questions about your status will not, on its own, be legally interpreted to say or prove anything in particular about your immigration status.
That said, you should definitely avoid saying that you are a U.S. citizen. Doing so could get you in a lot of trouble in the future.
Also: You should not run away from immigration officers, because, at least in some places, this behavior could be interpreted as evidence that you are an unauthorized immigrant. If you are approached by immigration officers, try your best to stay calm.
These tactics could still fail. Immigration officers may have other ways of determining your status. For example, if you are arrested, and you have ever had any immigration record, your fingerprints could help determine your identity.
Moreover, immigration officers may well be able to prove that you are an unauthorized immigrant without having to prove your nationality. For example, perhaps video surveillance clearly shows, or your travel companion have testified, that you entered the country illegally. At that point, assuming you are sent to an immigration court and you have no other basis to stay in the U.S., the immigration judge could still deport you to the country you last came from or (in the alternative) to any country that is willing to accept you.