You'll probably need to test this, but I think that all you technically have to do it save it into another directory. You could call it the same name, so that depending on how you're loading parts you may well have something to gain in terms of maintaining your existing assemblies.
Now if you want to simply unassociate it from the template, with the template and the member open, go into the spreadsheet, delete that particular record and save the spreadsheet and the template. It will give you a message that the member is being deleted from the template.
