I work as a Linux developer, and there actually isn't a system-wide clipboard! The window manager system (called "X") does a good job at hiding this fact to you, but if you try to copypaste text between terminals using Ctrl+K and Ctrl+Y you'll notice each terminal also has its own clipboard. Ctrl+Insert and Shift+Insert works in most programs, but not if you switch sessions to a "non-virtual" terminal...
Mac being an Unix system below all the DRM, probably has a similar situation.
With that said, you could use an extension to call functions from a C++ - compiled DLL (except they're called ".so" files in Linux) to access the X clipboard:
https://stackoverflow.com/questions/27378318/c-get-string-from-clipboard-on-linux
All of the suggestions in the accepted answer to that question are
programs, so probably most easily available as pre-compiled binaries, but if you can't find / be bothered to use their source, you could have the program as an included file, then also include a super simple "DLL" that just invokes the included-file version of the program and returns its output to the calling GameMaker program. (Just keep an eye on the licensing when including other people's programs!)