You can't disable it. The best you can do is disable some features. Actually, that's only the best you can do without rooting. If you really want to get rid of TouchWiz (and I understand if you do - I returned a new S5 because I hated TouchWiz so much), you need to root your S4 and flash a custom ROM. If you are still under warranty, this will most likely void it, and there is always a chance that you will brick your phone, but it's the only way to get rid of TouchWiz.
One other thing you can do without rooting is install a custom launcher, which can significantly change the user experience. I suggest checking out the Google Now, Nova, and/or Action launcher on Google Play and see if you like your phone better with one of them.