Tortise SVN is really just an easy way to access a Subversion repository. To quote the Subversion FAQ on how to remove a file permanently:
There are special cases where you
might want to destroy all evidence of
a file or commit. (Perhaps somebody
accidentally committed a confidential
document.) This isn't so easy, because
Subversion is deliberately designed to
never lose information. Revisions are
immutable trees which build upon one
another. Removing a revision from
history would cause a domino effect,
creating chaos in all subsequent
revisions and possibly invalidating
all working copies.
The project has plans, however, to
someday implement an svnadmin
obliterate command which would
accomplish the task of permanently
deleting information. (See
issue 516.)
In the meantime, your only recourse is
to svnadmin dump your repository, then
pipe the dumpfile through
svndumpfilter (excluding the bad path)
into an svnadmin load command. See
chapter 5
[ed: changed link]
of the Subversion book for
details about this.
Essentially, you're packaging the entire repository into a single file, running a command to remove all references to a given path from that package, and then turning that package into a new, different repository. Swap the old one in for the new one on the server, and you're good to go.
Except, as it mentions, all your client's working copies will probably be invalidated. And this does require being able to access the server. You are running your own SVN server, right?