Remove file from SVN repository without deleting local copy

svn delete --keep-local the_file

Rename your file, commit the changes including the "deleted" file, and don't include the new (renamed) file.

Rename your file back.

Deleting files and folders

If you want to delete an item from the repository, but keep it locally as an unversioned file/folder, use Extended Context Menu → Delete (keep local). You have to hold the Shift key while right clicking on the item in the explorer list pane (right pane) in order to see this in the extended context menu.

Delete completely:
right mouse click → Menu → Delete

Delete & Keep local:
Shift + right mouse click → Menu → Delete

In TortoiseSVN, you can also Shift + right-click to get a menu that includes "Delete (keep local)".