I'm not a lawyer, and don't play one on the YB, but obviously neither is your principal. The concept of double jeopardy is that you cannot be charged and punished for a crime that you have already been cleared of, or that you have already been convicted of - not that you cannot have a series of consequences for an action.

Someone sent to jail may also lose their job. Custody of their kids. The right to vote or possess a firearm. Etc. A drunk driver may spend time in jail. Lose their license. Be ordered to pay restitution for an accident they caused. Have their insurance go up. The law do not say that you only get to have one consequence for your actions.

I'm betting that the suspension already has multiple consequences. In my school, a student cannot attend school events while on suspension (or in-school suspension).

Tell your principal that he or she is an idiot. If they try to do more than one thing to you, point it out as proof that they are an idiot.