Cut off? Your hyperbole is getting the better of you. For a few days Mississippi inspected boats passing one point on the Mississippi River to see whether they were carrying troops or armament, then let the boats go on their way. Probably a wise move given how the North tried to send 200 armed troops into Charleston harbor a couple of days earlier. Mississippi stopped doing inspections after a few days. You used to incorrectly characterize the brief boat inspections as a blockade that cut off river traffic for months.
No one "cut off" the Mississippi until Lincoln succeeded in instigating war by sending a battle fleet to Charleston. In March 1861 Lincoln had tried, but failed, to instigate a shooting war by sending secret instructions to the Federal commander in Pensacola harbor to break a negotiated truce at Fort Pickens without telling the Confederates. Fortunately, the Federal commander in Pensacola harbor recognized the instructions to reinforce Pickens meant war and refused to do it, so Lincoln's war had to wait until April at Charleston.
But if cutting off the Mississippi was no threat because of the low level of exports passing down it, why was Sumter a threat to the confederacy?
Why was Sumter a threat to South Carolina? Sumter was an armed fort occupied by foreign troops within Confederate territory. Newspapers had been saying, correctly I might add, that those within the Lincoln administration advocating a course that would lead to war had gained the upper hand, and, if so, the fort was definitely a threat. And newspapers had alerted the South that a battle fleet was coming. The Lincoln administration lied about their plans to evacuate Sumter. "Gross perfidy" the Confederate commissioners in D.C. called it. But, wait. Lincoln said his battle fleet, inadequate for the task as it was, would only force their way into Sumter if the South tried to stop them. Who could trust Lincoln after his personal messenger Lamon and Seward had said the fort would be evacuated. Lincoln was doing his best to provoke war.
In contrast, Mississippi simply inspected boats for a few days to be sure they weren't carrying troops or canon that might harm Mississippi. River traffic was not "cut off."
Not really. For a short period the governor of Mississippi took it upon himself to blockade the river to Northern traffic, going so far as to fire on steamers. What was to stop him from deciding to do it again?
No one "cut off" the Mississippi until Lincoln succeeded in instigating war by sending a battle fleet to Charleston.
You mean when Davis used Sumter as an excuse to start his war, don't you?
Sumter was an armed fort occupied by foreign troops within Confederate territory.
Sumter was no more a threat to the confederacy than Guantanamo Bay is to Cuba.