You can do that if you have root
The app Pdroid can block a number of permissions in that way, but requires Root.
I combine that with Avast AV which contains an application firewall, also requires root. It allows Deny All, Permit by Exception. If it is a game or something that has no need to access the internet it is blocked automaticlly, unless I specifically add it to the allowed list. If it needs internet to work I use Pdroid, so for example, facebook is feed a random Device ID, phone number, SIM serial, Subscriber ID, GPS and Network location, while incoming number (why the hell do they need this?), call log, SMS, MMS, Sim Info, and network info are blocked completely.
I know some friends who would really love these capabilites, but are nervous about rooting their phone. It would be great if this was allowed for everyone.