How can I remove a cable from a junction box?
NEC officially says abandoned wire/cable should be removed altogether from the box, and the walls, and if that is not practicable, then utterly destroy it where it is reachable. 

Fortunately, they don't say that about conduit, because I have loads of conduit routes I'm not using right now, that I prefer to keep in place for future use.  

Even though you don't envision a need right now, fact is, you never really know. 

So I recommend exactly what JACK is telling you: remove them from the picture non-destructively so you are able to spare yourself the expense of fishing wire if you ever need them in the future.  

One of the numerous opinions on the forum you linked recommended pushing it just outside the junction box, but where it could be reached if you wanted it in the future, and then if needed cover any empty holes with a knockout cover. (about 10 cents).  I would do either that, or what Jack says - just cap it off and don't worry about it. 

The only exception is if retaining the cable exceeds the cubic-inch limit of the box; that must be dealt with either by adding a box extension or pushing the cable out of the box.