How to clip overlapping paths?

At the bottom of this escutcheon, I tried to join two paths.   They ended up overlapping each other.  How do I cut off those little pieces? (They are at the pointy end of the sheild) I tried a clipping mask, but that did not work.  Should I just go back and redraw it?  Of course I didn't notice it until I went to turn it into a pdf!