What would happen if you cut the optic chiasm?

Blindness. Injury to the optic chiasm will produce partial or total blindness.
Don't do this. The chiasm is where the optic nerve fibers from each eye meet and cross the fibers. It is the visual cable to the brain. If you cut it completly, blindness is the result. Compression occurs by various tumors mostly of pituitary origin which can cause visual loss as if a portion of the nerve were cut.