Hello!
If you really want the phone not using mobile data your best choice is to disable mobile data. It is not clear what you call sleeping in your question. Is it you or the phone? If it is you (night sleep) the best way to preserve phone battery at night is simply to enable plane mode during night. I do this and the my phone usually use 1 to 3% of battery during a whole night. (My phone is a GS5 but you get the idea).
If you are worried about the phone data/power consumption while it is not used what you can do is install an app called gsam battery monitor (sorry I cannot post links) which will provide you details about what app/stuff consummed battery (and data). This can help you detect if an application is consumming a lot of data. You also have more basic information in the phone settings.
Most of the "big" data consummer app have setting so that they do not use mobile data but wifi instead (eg drop box, photo upload,...).
Hope this helps.
JM