According to the US Constitution, the US Supreme Court has original jurisdiction in "all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party". Original jurisdiction of the US Supreme Court cannot be limited (nor expanded) by the US Congress, but the appellate jurisdiction can.
My understanding is as follows: the US Supreme Court's original jurisdiction is not necessarily exclusive, and thus other courts can also have original jurisdiction over these cases, which is known as concurrent jurisdiction. The plaintiff can thus choose the court in which he files the lawsuit. If the plaintiff chose to start the case not in the US Supreme Court, but rather in another court having original jurisdiction, then the US Supreme Court could have only appellate jurisdiction over such case.
Is it correct?
If so, could the US Congress strip the US Supreme Court of appellate jurisdiction over cases over which the US Supreme Court has original jurisdiction?
Edit: In an already deleted answer, It was argued that SCOTUS' original and appellate jurisdiction is mutually-exclusive, according to Marbury v. Madison. However, it seems that SCOTUS has rejected this argument in Cohens v. Virginia in which SCOTUS held that "where the words admit of appellate jurisdiction, the power to take cognizance of the suit originally does not necessarily negative the power to decide upon it on an appeal, if it may originate in a different Court" and "The general expressions in the case of Marbury v. Madison must be understood with the limitations which are given to them in this opinion".