You could run the svn export
command to download the data without the .svn directory. However, you cannot use the exported data to commit, update or diff it with other versions from the repository.
Subversion stores metadata and the pristine versions of files in the .svn directory of a working copy. This allows you to perform offline version-control operations with the Subversion client (i.e., you can revert or diff files without contacting your server).
Note that there is an ongoing work to make some parts of the .svn directory optional and therefore minimize its size (see ticket #525 and https://mail-archives.apache.org/mod_mbox/subversion-dev/202107.mbox/%3c874kcf6xin.fsf@red-bean.com%3e).
Update #1:
As Alvaro Gonzales noted (the comment is now deleted), you may want to consider sparse checkouts. I don't think that's what you are looking for, but check this thread Can you do a partial checkout with Subversion?.