If a diplomat is going on a shooting spree they can be shot and killed with no ensuing issues as a result of US law enforcement enforcing laws in the moment. If they are robbing a seven-eleven they can be arrested and held until arraignment. They can be ordered to remain in their home, aka house arrest. They can be ordered to leave and they have no option to remain in the country. The US constitution does not grant diplomats immunity it is something we have agreed to via treaty and law. They are 100% subject to our laws, that's why our law granting them immunity applies.
That flies in the face of what I understand is true about diplomatic immunity. Citation required.
As a less extreme example, diplomats can and DO park their vehicles illegally: in No Parking zones, Handicap Only zones, and blocking fire hydrants. Diplomat plates render the police unable to ticket them. It's civil not criminal courts, but for the exact reason that they are immune to our laws.