Question: On this Windows 10 machine, from time to time the clipboard goes really wonky. Not only can I not paste anything, but just trying to copy can cause apps like Edge to blow up. Restarting the machine solves the problem, but feels like overkill to me. I'm one of those people who has a lot of things open that I will "get to" in the next week or so, and they don't all re-open after a restart.

I'm comfortable at a command prompt, or using the services app or task manager, so if there was a process I could reset or restart that would give me my clipboard back, I'd be really happy. 

FWIW there is no VPN or remote desktop involved here. I'm just bumping along, using my machine, running assorted Office things, lots of browsers, Slack, Skype, Discord, a bunch of Notepad, and after a while I notice I no longer have a clipboard.

Answer: 
The clipboard becoming inaccessible is usually because some app is holding
exclusive access to it.

You may test it by, first, logging in and out, then by selectively killing
tasks. If the clipboard becomes accessible again, then you have verified
that this is indeed the cause.

Microsoft products such as Word do not normally suffer from such problems
(unless extensions were added).
It is more likely to be some installed browser extension.
You may selectively disable these extensions until the malfunctioning one
is found.
If you are just trying to clear the clipboard you can use either of the below

Command Prompt : `echo off | clip`

PowerShell : `Set-Clipboard`

Above two commands will clear the clipboard contents but can't promise this will really solve the problem.