Lazermonkey,
I am really glad you asked that question.  When I went to my 4x4 to get my tire repair tools, I learned that they had migrated to a place I would have never guessed.  <img src="/images/graemlins/blush.gif" alt="" />  Fortunately that happened at home where my older son was able to redirect me to where he had moved the tools  before I actually needed the them.
Anyway to get to your question,  my kit  uses a patch which looks like a pipe cleaner.  After inserting the patch,  you do indeed clip it off flush with the surface of the tire.  I also saw a mechanic do that and then finish with a quick burn of a butane lighter of any protruding material.  His patch worked fine.
Good luck,
John