Yes, it does; the corpus callosum is a major communication pathway between the hemispheres. Severing the corpus callosum is only done when seizures are severe enough to warrant it, and other options are ruled out for various reasons.
The condition of having a severed corpus callosum is often referred to as being a split-brain patient. There are some individual differences between patients, but hopefully searches using the keyword "split-brain" can help you find tons more information (summarizing it all here would give much too long of an answer).
One thing that is important to keep in mind is that although the corpus callosum is a very substantial connecting pathway between the hemispheres, it is not the only one, so the hemispheres are not completely severed. The cortex also communicates substantially with other brain structures that are not directly impacted by severing the corpus callosum.