If it cut off someone's finger, it had to be sharp.
Not really- all you have to do is apply enough force to a small enough point.
Go buy a cheap ham or a chicken. Swing a 3' long, 1 1/2" wide, 1/8" thick unsharpened piece of metal at it and see if you don't do some damage...
I wouldn't be surprised if you couldn't take a swing at the chicken in the air (like swinging at a baseball) and chop something off of it, especially if you do a 2 handed strike.
(Of course, I wouldn't expect a souvenir weapon to be good for more than 1-2 of solid hits before breaking or otherwise dissembling itself.)
This is why branch cutters aren't simply just a sharp blade, but two blades (like scissors).
A branch has a very different structure from a hand. A branch is a relatively homogeneous structure of cells with firm cellular walls and a hard exterior. The fibrous nature of a branch is very resistant to cutting.
In contrast, a hand is made up of a LOT of soft tissue around bone. Flesh isn't really designed to resist cutting. Cartilage is tough & spongy, but tears fairly easily. Bone is very, very strong- thigh bones have been shown to withstand crushing forces (along the long axis) of TONS before breaking. However, only a few pounds of pressure need be applied across the short axis of a bone to break it, as I found out- I broke my thumb blocking a pass when the point of the ball hit it squarely. The tiny bones of the hand and feet are not particularly strong.
If the blade intersected with the hand at or near a joint, fingers could be lopped off quite easily. With enough force, the same could happen even at the center of the bone, cleaving it in two.
BTW, for the record "Burglarize" appears in my Websters's Deluxe Unabridged Dictionary...y'know- one of those 10lb beasts? It does not, however, reveal WHEN it became a word.