How can I block an app from accessing the internet completely?
You mention in your comment to @LouisGR that you're just trying to block WhatsApp for a while, while also using other apps. That's easy enough.
Disable the app from running in the background. As long as WhatsApp isn't in the foreground, it won't run at all and therefore can't access data. To do this, go to Settings, search for "Background apps", and turn off the toggle for WhatsApp. Make sure to turn this back on later, though, if you want the app to be able to receive message or call notifications while not running in the foreground.
As there is no firewall to control app access to the Internet. I have also tried to find any option natively in Windows Mobile but I have found none.
The only solution I can think of is to activate power saving mode. Choosing this option will curb all background activities for most apps even accessing the internet. The second step, never touch or open the app you don't want to access the web. The only downside for it that I have to sync the other apps I use manually.