OK, blocking all mobile data would be much easier since you could just disable it when needed but to have just one app accessing mobile data and blocking everything else is more involved. A basic firewall app will do what you want, but it's going to involve some work on your part to implement it the way you want.
A firewall app allows you to selectively enable/disable online connectivity for WiFi and for mobile data, for each of your installed apps, and conditionally when it involves some system-level, pre-installed apps. (with a non-rooted device your options for system-level apps/services will be limited, for a rooted device you have more control over more services). But in either case, when you initially install and start configuring your chosen firewall app, expect to spend some time getting it set up accordingly.
There are several firewall apps to chose from, for a non-rooted device I'll suggest you try NetGuard, it's an Open Source project (no back end ties to a specific corporation), actively developed and supported, and it has a really good feature set.
https://play.google.com/store/apps/details?id=eu.faircode.netguard&hl=en_US
(..... the NonRoot Firewall app gets a lot of press and recommendations but note there are some caveats -- development for it was abandoned for over five years and only recently been picked up again by its developer, and according to its Play Store page, it still has issues with support for IPv6/LTE connectivity.)
For a rooted device, I highly recommend the AFWall+ firewall app. It's also an actively developed and supported Open Source project, and being a root-required firewall is able to rely upon iptables, the integral firewall service that's a part of the Android kernel itself.
https://play.google.com/store/apps/details?id=dev.ukanth.ufirewall&hl=en_US
That's also a notable issue you need to be aware of, while root-required firewalls can just use iptables, all the non-root firewalls not having system-level permissions are also not able access a system-level service like iptables. Instead, non-root firewalls rely upon a clever workaround. They use a local VPN service instead, emphasis on 'local'. This VPN isn't what most people expect where it involves one to pay for an account and it uses online servers as its back end connectivity, this is just a VPN service that's running only within your device that the non-root firewalls use to redirect outgoing traffic through. This local VPN is what's used to filter what does and doesn't get online access. It works well as is but the problem is if you have one of those conventional VPN services, you cannot have both a non-root firewall app and your VPN service running at the same time, It's an either/or matter. Unless your device is rooted (just assuming it is not) this local VPN workaround is also what a lot of other apps like non-root ad-blockers rely upon so if you're already using either of those things than this won't work out for you.
