Voce pode ter dado permissão de escrita, mas o próprio sistema de arquivos do seu HD externo esta montado como "somente leitura" (ro).
Alguns HDs externos, possuem uma "chave de segurança", veja se o seu tem essa função.
Tente o comando:
 mount -o remount,rw 
 -o     Options are specified with a -o flag followed by a comma separated string of options.
 -w     Mount the filesystem read/write. This is the default. A synonym is -o rw
remount
              Attempt to remount an already-mounted filesystem.  This is commonly used to change the mount flags
              for a filesystem, especially to make a readonly filesystem writeable. It does not change device or
              mount point.
              The remount functionality follows the standard way how the mount command works with  options  from
              fstab.  It  means  the  mount  command doesn't read fstab (or mtab) only when a device and dir are
              fully specified.
              mount -o remount,rw /dev/foo /dir
              After this call all old mount options are replaced and arbitrary  stuff  from  fstab  is  ignored,
              except the loop= option which is internally generated and maintained by the mount command.
              mount -o remount,rw  /dir
              After  this  call  mount  reads fstab (or mtab) and merges these options with options from command
              line ( -o ).
       ro     Mount the filesystem read-only.
       rw     Mount the filesystem read-write.
Veja o man do mount: # man mount