You don't need write permissions, because what you're describing is not very reasonable. Imagine we are talking about copies of the data. Would you expect to have a magic command to wipe out all copies of "your" data? Well, if you're the RIAA you would, but it would be unreasonable.
If you have write permissions, you can wipe the file contents clean and destroy your links. Others will still be able to open the file, but the data would not be there anymore. If you have read permissions, then all you can do is remove your link.