There is no specific operation in SVN as branching, all operations (tagging, branching) are just essentially making copies within SVN repository (however on SVN server these are not separate copies, i.e. you are not doubling space on server side, but instead the cost is almost nothing). So, all you need is just copy it to another location and start working there:
$ svn copy svn://host.example.com/repos/project/trunk \
svn://host.example.com/repos/new_project/trunk \
-m "Creating a new_project based on project"
After that, you probably would want to switch local working copy to point to the new_project location on the repository:
$ svn svn switch svn://host.example.com/repos/new_project/trunk .