According to the documentation for svndumpfilter, you can include one subcommand when filtering a dumped repository. Suppose you have a repository that has a path "/some/path" that you'd like to separate out into its own new repository. From the documentation, you simply pipe the original dumped repository through the svndumpfilter command.
cat repos-dumpfile | svndumpfilter include some/path > new-dumpfile
The caveat is that if there are paths copied from other paths in your repository that the include argument does not cover, you'll get an error. I got around this command by piping the output from one svndumpfilter command to another, each with exclude commands instead of include commands. The result leaves only the paths I want, but included the alternate copy branch that I had used part way through the coding process.
cat repos-dumfile | svndumpfilter exclude unwanted/one | svndumpfilter exclude unwanted/two | svndumpfilter exclude unwanted/three --drop-empty-revs --renumber-revs > new-dumpfile
Notice on the last svndumpfilter command, I added a couple arguments to renumber the repository revisions and drop the empty revisions. While these are of course optional, in my opinion, they make the new repository cleaner.
The subversion book states you can edit the Node-Path values in the dumped file to have the new repository imported at different paths. I chose to simply issue an "svn mv" command once I imported the repository.