[corvus_sapiens]

There are 250 million neurons in the corpus callosum, each with a diameter on the order of microns. Individually, each one transmits a very primitive signal (think biological bit) that doesn't mean much without the other millions of neurons. It's extremely complex and thus extremely frail. If the cut halves on both sides don't line up exactly, you have the equivalent of static. You wouldn't mash two cut ends of normal data cables together, and there are only on the order of 100 "neurons" there.

What you say is theoretically possible if the neurons weren't living cells and humans had the technology to reconstruct the brain's wirings. Your body isn't going to figure out which "wire" connects to which on its own.