I can't create a reference in the one-part assembly because it has a reference in another assembly. However, I created another piece without even going after a copy and SW always tells me this pb. How does this link directly break?
On your part, point to the sketch or feature that has the external reference to be deleted, right-click, "External references".
There you see all the external references of this sketch or function > "Break everything".
A ">x" sign will appear on sketches or functions whose references have been broken.
PS: if you still want to draw your part in several contexts, you must check the following option: Tools/Options/External references, "Allow multiple contexts for parts when editing in an assembly"