My S4 mini is the Canadian edition SGH-I257M. It is a stock configuration, no rooting, flashing, etc. I have disabled 50 apps and hope to be disabling more. These stay disabled thru power off-on, including remove/re-install of the battery. These include Adapt Sound, BlurbCheckout, ChatOn, DropBox, Google Play [Books, Games, Magazines, etc], Google+, S [Memo, Translator, Voice, etc], Samsung [Books, Link, Push Service, etc], SNS, and Yahoo! News to name just some.
The phone has a Disable option. This is not TurnOff or Stop or whatever, but Disable. It works ...
Settings | More | App Manager | All then tap an App, and the options include ForceStop, Disable, and Show Notifications. There are some Apps for which the Disable option is grayed out so it is not available. I have not finished with this process yet so i am unable to characterize which that applies to. A few are - AllShare ControlShare, Android System, BlueTooth Test, etc. A quick run thru parts of the list looks like i would not want to disable those anyway.
So, so far 50 apps disabled. The list is in my other thread that i referenced in post #2. More on the way [i hope].
Mick