SCOTUS, Jury Trials, Diplomatic Immunity: Legal Eagles?

[AZRedhawk44]

So, I was googling around and looking for numbers on exactly how many times the US Supreme Court had actually utilized a Jury in any proceedings before it.  That John Jay tidbit in the Montana Juror thread got me curious.

I stumbled across this:

U.S. CONST. art. III, § 2: "In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction."

I thought that Ambassadors could exercise diplomatic immunity.

Who would have jurisdiction to DRAG an ambassador before SCOTUS?

Or would an ambassador have free rein to go on a knifing spree until SCOTUS was somehow notified and issued a bench warrant?

And... does anyone know how many times SCOTUS has selected a jury for a trial?  That would be quite a privilege to be part of, methinks.

[Regolith]

Maybe they mean US Ambassadors rather than foreign ones? As in, if one of our ambassadors does something illegal while at a US embassy, the Supreme Court gets jurisdiction over the case.

Just a guess.

Edit: Or perhaps they get jurisdiction when the ambassador's host country waves diplomatic immunity for the ambassador.  Or both.