svn co http://mysvn/myproject /path/working-copy/myproject

On post commit:

svn update /path/working-copy/myproject (update working copy)
mv /path/deploy/myproject /path/deploy/myproject.bkp (backup old deploy)
svn export /path/working-copy/myproject /path/deploy/myproject (export from working copy)

I think a svn update and an export of a working copy are faster than a full new checkout or a full remote export…