It is possible to do but not simple. I assume when you say mobile devices, this includes both Android and iOS.
This functionality is not build into Unity. There are two steps to do this:
What to do:
1.Disable Wifi
2.Disable Mobile Data
The entire internet connection should be killed when you do both of this.
How to do it:
You will have to make a plugin to do this. This is platform dependent and you must know basic Java (for Android) and Object-C(for iOS) in order to do this.
Google "How to disable wifi on Android with Java" and also "How to disable mobile data on Android with Java". Convert that into a plugin. That's basically a simple function that you can call from C# to toggle wifi or mobile data on/off.
Do the-same thing for iOS. Take the Object-C code and turn into a plugin then call it from C#.
As for how to build the plugin for each platform, this can be found with a little bit of research. There is no other way to do this. My other post shows how to enable/disable wifi on Android only but that's just part of what to do in this answer. You still need a way to disable mobile data.