A patch for this had been posted before, though I don't know it can delete. It can add documents and commit from admin gui.
https://issues.apache.org/jira/browse/SOLR-85 Koji JLIST wrote:
It seems that the web interface only supports select but not delete. Is it possible to do delete from the browser? It would be nice to be able to do delete and commit, and even post (put XML in an html form) from the admin web interface :) Also, does delete have to be a POST? A GET should do.