I am stopped by the program when trying to delete a global variable
Why delete? Change its value!
I don’t need that variable anymore, and I want to remove it from the game
You cannot remove a variable, because if a variable doesn’t exist, its value is 0 (therefore, it exists 
).
So you should change its value to zero, as said above.
I keep closing the program when deleting a global variable
This looks like a bug.
From reading your original post I thought you wanted to remove a global variable during game play - and my first reaction was the same as @FreakishSky96.
In fact you are in the IDE and use the remove button to get rid of that variable. For whatever reason there is a runtime error. I cannot fix that error, but as a workaround you could close GDevelop and open game.json in any text editor to remove the corresponding line.
@all Is there some documentation of the structure of this json file?
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Can you report the issue on github please, with the button after the crash.
And add the link of your video with it.
oh my, I was way offtrack 
Let’s move this to bug reports.