Just to prove it once and for all:
http://i.imgur.com/NLzdQi2.pnghttp://i.imgur.com/Njlbz7w.png
Both types of fatal finishes right there.
The thing with the throat-slitting one is that the enemy MUST BE on a standing position (not jumping, not crouching, etc) and NOT defending himself (which is hard to achieve against the CPU in normal difficulty or higher).
The strength of the slice attack doesn't matter, but if you're too close to your opponent you're likely to drop him down to floor (which breaks the standing position condition) instead of slice him.
I think the conditions are the same for the arcade game, and I find them very logical. To stand in front of your opponent while not ready to defend yourself is a fatal mistake in a sword duel.
The best way to pull it off against the CPU is to counter-attack them right when they're back to the stand position or to jump to their opposite side after they've already started a special or strong standing attack (this is how I achieved the screenshot above) and then attack with a slice move (the opponent will be, obviously, not blocking any attacks).