Trouble exporting to AI file

Hey all, I’ve tried doing a search to see if I can figure this out, but it seems to me something has changed in the last few years and nothing suggested is an option anymore. 

I have an illustrator file with several things in it, but I would like to be able to save a copy with only what is on the artboard. I have seen this done before, and people in the past seem to have been able to do it, but i’ve tried everything I can find and can’t seem to manage it. 

I have tried saving a copy, exporting for screens (does work but can’t be opened by anyone else, comes up with an error page when someone tries to open), save as > export artboards, just about everything out there. The only other workaround I can think of is to make a copy of the file and just delete everything else several times over for all the different things I want a copy of, but that seems more tedious then it needs to be and I would like to see if I can do something better in future as well.

Thanks!