I am using Samsung Galaxy Grand 2 without rooting. In a nutshell, I want to disable the Internet specifically for WhatsApp so no new message/notification/media will arrive on my phone despite mobile data/WiFi being turned on. How can I do it?
Stop using WhatsApp is the best solution you get. In the worst case you could stop getting notifications here
Settings>Apps>WhatsApp>Stop notifications but you can not stop getting messages when the app is open.
A free suggestion would be - use separate Instant Messaging services (IMs) for each one because we've got so many of them like Telegram, Hangouts, Viber, Line, WeChat, etc etc.
This may sound trivial but if your goal is to only stop receiving notifications by restricting Internet access to Whatsapp until you use the app again, then why not consider killing the app. There are many apps available for such.
Otherwise, you can go to Settings -> Apps -> Whatsapp -> Force Stop ; Or
In the launcher, hold the Whatsapp icon until you see App info option and slide the icon into it. From there, kill the app.
If you use a firewall app like suggested in other answers, they will still require user intervention, so more or less, killing it natively is best than installing them which may collect user data for development/commercial purpose.
You can also automate the process of killing the app when not in use through apps like Automateit or Tasker.
It is obvious that this won't work if you happen to use Whatsapp to see messages but not want it to use Internet. Then firewall is your only choice.