Did not have luck with these examples:
Javascript File remove
Javascript FSO DeleteFile Method
Deleting a File
There are no special permissions on the fi
If you are doing this in a RESTFUL way, you would send an HTTP DELETE request.
jQuery's ajax method states that you can use the method parameter to specify 'DELETE' but notes that some browsers may not support it.
Obviously you will need a webserver which will accept a DELETE request, and apply some sort of authentication/authorization so that joe random visitor can't delete your files. I believe Apache's mod_dav will get you started here.