If you do not have an LSposed framework or similar (formerly knows as Xposed Framework) you can either use Adaway for blocking the phone from reaching websites (keep in mind that this is globally, though) or e.g. AFWall+ for preventing single Apps to connect to the internet (Apps that don’t try to get internet access are not shown is the list provided by AFWall+).
If you have LSposed or similar I believe it is possible to install XprivacyLua. This was/is(?) a very powerful tool to manage every single access an app is trying to get. Why would a sketchy chinese calculator app need access to the contacts and the internet even though this was never allowed in the system settings?