Touchwiz is not just the launcher, it is an entire framework they have built into Android. It controls the notifications, the settings, the whole OS is basically Touchwiz throughout.
Samsung do not provide the stock launcher with the device (Like old HTC devices used to) so if you remove it you will just have no launcher, no way to open apps etc. You could just install Apex, Nova, Google Now or whatever launcher before doing this, and freeze the launcher rather than completely delete it to ensure there is no unexpected outcome(s). Generally it will either default to whatever launcher is installed, or it will give you the 'Choose your launcher' screen where you can accept whatever one you want and click "Once only" or "Always" as you do with other apps.
As Touchwiz is the framework, you would need to remove the whole ROM from the device and install a Non-Touchwiz ROM like AOSP, CyaongenMod, Google Play Edition (if your device has one) and so on.
Note: any changing of frameworks in Android can completely brick your device, so proceed with caution and make nandroid backups! You can never have too many backups!
Note 2: you could remove all of Touchwiz and rebuild the ROM, but that would be way outside the remit of this site. It would probably be reinventing the wheel anyway and there are plenty of AOSP ROMs about.