use the "unlink" command and make sure not to have the / at the end
$ unlink mySymLink
unlink() deletes a name from the file system. If that name was the last link to a file and no processes have the file open the file is deleted and the space it was using is made available for reuse. If the name was the last link to a file but any processes still have the file open the file will remain in existence until the last file descriptor referring to it is closed.
I think this may be problematic if I'm reading it correctly.
If the name referred to a symbolic link the link is removed.
If the name referred to a socket, fifo or device the name for it is removed but processes which have the object open may continue to use it.