I am wondering if there is any way to save a configuration of an assembly as its own separate assembly? This new assembly would NOT include suppressed or hidden components in it's parents assembly.
Welcome to SolidWorks forums Caleb.
Make a copy or do a save as of your current assembly with the required name. Now simply delete the parts and other configurations you don't want. Please note that if you that configuration referenced to any other assembly or drawing, that may get broken since you'll be deleting this configuration from the parent assembly file.
You might also find this post helpful for your future reference
I am not aware of an automatic way to do this.
but you can do a save-as, delete other configs, and then delete anything that is suppressed.
if you do this a lot, I expect a macro could be written (though I have NO experience with macros).
Retrieving data ...