An urumi is more like a flexible sword than a whip.
I imagine you would slit their throat with the many segmented blades.
An urumi is made of metal ribbons attached to a sword-like handle. You could call it a flexible sword in the same sense that you could call a capybara a "big rat". Technically accurate, but not what most people would say. They'd call it a whip.
As far as how one would coup de gras with an urumi, I'd say Barathos has the right idea, flaying flesh from the neck would expose important blood vessels.
It's a whip sword. It's both a whip and a sword in equal measure. There, we're all happy.
And I think we all agree that the coup de grace involves going for the neck.
A whip sword is what Ivy uses in Soulcalibur. :P
On a somewhat tangential note: there's an interesting scene showing an urumi being used in the (Bollywood) movie Ashoka. Not used to cut any necks though, sadly.