I didn't know the term, but comparing this picture of something called a "beaver blade handle"...

...and this picture of a beaver's tail...

...I'm tempted to think it refers to the knurling (a manufacturing process, typically conducted on a lathe, whereby a diamond-shaped (criss-cross) pattern is cut or rolled into metal).
But it's probably relevant to note that Beaver® has been manufacturing high-quality, trusted surgical blades since 1932.
EDIT: I'll leave the above for historical reasons, but since someone downvoted I spent a couple more minutes looking into this. Here's a relevant definition for OP's (original) context...
Some surgeons prefer to cut the ear canal skin flap sharply using a beaver blade or sickle knife
- see right picture.
...and here's the picture...

(And no - I've no idea why they call it a "beaver" blade, though "sickle knife" is obvious!)
EDIT2: Okay - I'll hazard a guess it's because beavers' teeth are curved, a bit like a sickle.