Entering this command in Terminal and restarting the Mac cleared up the issue for me:
sudo update_dyld_shared_cache
It will ask you for your admin password, which you enter and hit "Return".
Let it run until it is done (it will spit out a bunch of "warnings" - DO NOT BE ALARMED, THIS IS NORMAL).
Then restart your Mac.
Because nobody every runs a Terminal command without knowing what it does (!!!), right?, here's the low-down:
WHAT IT DOES:
It updates the listing of shared system services used by various applications ("dynamic linker").
Simplified explanation:
When any application uses a function supplied by the operating system, it needs to reference, look up, and dynamically load the system library that actually performs that function. This can take time, so every time you install software or first run it, the system looks up all the libraries it requires and puts them in a list linking them to that app (in earlier systems, this was called "update prebinding", these days, it's what happens when you see "optimising system").
This saves a lot of time later on and speeds up performance.
Apparently, a bug in High Sierra can cause the libraries needed for copy and paste (the clipboard) to get disconnected from the list of services, the dynamic linker daemon database.
So forcing the system to re-check all of that database (dyld cache) will restore this functionality.