Someone else asked this question a while ago about their S4, I copied the two best answers and reposted them below. Short version - to really get rid of TouchWiz you need to root your phone. If you’ve rooted it, you can flash a custom ROM. The Google Play edition ROM is free of TouchWiz and let’s you enjoy a much more pure Android experience. You can also install a custom launcher such as Go or Nova from the Play Store, but they will just mask some of TouchWiz, they won’t really get rid of it.
According to Walrusman:
"The problem is in the calendar app. First, trash the icons on your home screen and disable and calendar widgets. Next go into your application manager and select the calendar app. Force stop it, disable it, clear the data and the cache. Do the same thing for the widget if it has an icon. Basically, you do want anything with the calendar running or active. You may need to restart your phone but I didn't. As soon as I did all of the the stupid TouchWiz stopped popping up. Good luck!! Hope this helps."
"The only way I know of is to root the device and flash a custom ROM. The way to avoid it in the first place is to buy the unlocked Google Play version, but you are going to have to ante up $649 for that. You can just turn off some features such as Motion and Air Gesture, but you can’t turn off TouchWiz. I think it is installed on the /system partition but I would have to check to be certain, and I don’t have an S4 nearby."