If you're using it right, the punchdown tools should trim them off for you.
But to answer your question, yes, they should be trimmed flush.
Are you using the right end of the blade? One end has a sharp edge , the other end doesn't. the sharp edge will go toward the light side of the tool (it will only fit in one way). The side that has "Cut" printed on it will have the sharp edge.
Good Luck .....Cat6 eh?
Scott