If you trigger a Finishing Blow during a Duel to First Blood you perform a Critical Strike against your opponent. However, since a Finishing Blow does no damage the opponent never receives wounds greater than their threshold and thus never become incapacitated. Since the opponent was never incapacitated, the Finishing Blow doesn't end the duel immediately (the duels objective was never met). So, you end up in a weird situation where you can cut off someones arm in a Duel to First Blood and yet the duel must continue....
The same is true for Duels to First Strike since no damage is ever dealt.
Independent of this, It seems weird that a "Duel to First Blood" continues with both duelists hitting each other repeatedly until one is beaten down.