In a join table, the join records are the "relationship". So when you want to unlink two parent records, you actually delete the join table record, not the relationship. (Relationships can't be deleted via scripting.)
So, to accomplish what you want, your script might look something like this:
If [ not IsEmpty ( SoftwareAsset_Assignment::id_asset ) ] // Use any field in the join table that will always have a value
Go to Related Record // Use a layout based on the join table
Delete All Records [ No dialog ]
Go to Layout [ original layout ]
This worked! Thank you so much.