From FCKeditor Docs

DeleteFile

Deletes a file.

Sample Request

In the root directory of the resource type “Files”, delete the file “Test.jpg”.

connector.php?command=DeleteFile&type=Files&currentFolder=%2F&FileName=Test.jpg

Sample Response

<?xml version="1.0" encoding="utf-8"?>
<Connector resourceType="Files">
 <Error number="0" />
 <CurrentFolder path="/" url="/userfiles/files/" acl="255" />
 <DeletedFile name="Test.jpg" />
</Connector>

Note that the file names may contain non ASC-II chars.