I've seen plenty of people using the phrase "cut the Confederacy in half" with regards to Grant taking the rest of the Mississippi River in 1863, and how it was a great loss to the Confederacy.
But it wasn't anywhere near half. By states, it was 2 cut off from 9. By population, it was a little over 1 million on the west side, 8 million on the east side. I don't know how to tell whether they produced any useful supplies for the rest of the Confederacy. By transport, there were hardly any railroads crossing the Mississippi River ( http://railroads.unl.edu/views/item/1864rr?p=2 : includes gauges!), so almost all supplies would have gone by rivers to the Mississippi or the ocean; the previous loss of New Orleans and the increasing US blockade would have blocked ocean travel anyway. I wonder whether the main value of the Mississippi River was to allow the US Midwest to export abroad ... except that they could do that already with the Great Lakes + Erie Canal, or by the extensive railroad network.
So why is it said to have been a great blow?
Edits: (1) About the stated importance: Grant in his Memoirs, I, 567, wrote "the fate of the Confederacy was sealed when Vicksburg fell". McPherson quotes that when writing "The capture of Vicksburg was the most important northern strategic victory of the war".
(2) /u/free_world33's assertion (removed) provokes a question. I wonder if it's a separate top-level question or a/the major followon here. In 1860, what trade happened across the Mississippi River, where did it come from, where did it go? What trade happened along it, where did it come from, where did it go?
You are correct in the assertion that geographically, the Confederacy wasn't split in "half," but it was irreparably split. Think of the consequences had the British been successful in controlling the entire Hudson River and split New England from the other colonies. Geographically it wasn't half, but would have been a decisive blow.
Vicksburg was vital for two reasons. One, it was a southern bastion that had to be taken to effectively control the River. The Union could not simply bypass it, and they couldn't ignore it, so it had to fall. Two, the Mississippi was vitally important to the transport of goods and materiel for around ten states. The Ohio, Missouri, Tennessee, and Cumberland Rivers, plus the Red River all flow into the Mississippi. Granted several parts of these were in seceded states, but goods moved to and from Indiana, Ohio, Illinois, and Missouri all needed the Mississippi to move and obtain goods. Railroads were in place, but much of the midwest did not have easy access to the Great Lakes, mainly since the MS River was there to use (until it wasn't). Vicksburg was on a high bluff at a hairpin turn, and after New Orleans, Memphis, and Island No. 10 fell, Vicksburg was the last blockage to allowing Union forces and gunboats to move men and supplies to other vital areas much faster. And with complete control of the River, Richmond no longer had any real control over anything in a large section of the Confederacy. Texas did supply a large number of soldiers in the Confederate Armies, as well as being a vital route to funnel (i.e. smuggle) goods from ports in Mexico.
It's also important to remember the Mississippi River wasn't the only valuable objective. By July 1863, The Union controlled the entire Cumberland River, and the majority of the Tennessee (which is why the Emancipation Proclamation didn't cover Tennessee, as it was technically under Union control then), New Orleans, parts of North Carolina, West Virginia, Kentucky and Missouri (which had remained in the Union officially but had many occupying Confederate forces early on). In other words, Vicksburg was one of the last major waterways the Union needed to seal the fate of the Confederacy. On its own, it wasn't quite THAT important, but taken as a whole, the Confederacy was doomed by losing its rivers, the Mississippi being one of them.