Blazej is correct, just navigate to the Story issue that you want to remove from the Epic, and scroll down to the "Links" section - there you can see any Epics the Story is linked to. Just click the garbage can icon to remove the link. Not sure what function you are using, as your description is strange - maybe you can post a screenshot of what you're doing when you try to follow those instructions?
You have to put the "epic link" field on the screen. To do that you need administrator rights. Go to the project administration page. Click "screens". Click on the screen that is set for the story issue type and to "Edit" operation. add "Epic link" field to the list. It will be saved immediatly, no need to confirm. Once again edit the story you wish to remove from Epic and look for the added field. Erase the content of the field.
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