Oddjob's hat should've at least cut Tilly's skin

I think the OP was referring to the discrepancy between what the hat did to the statue versus what it appeared to do to the girl. On the one hand, the hat literally lops the head off of a stone sculpture, but then doesn't even draw blood when killing the girl.

Honestly, the way the scene was done confused me a bit as well. Since the thrown hat didn't decapitate the girl like it did the statue, nor even draw blood, I was initially wondering if the girl was actually dead, or somehow just knocked unconscious.

I believe it ultimately came down to a simple issue of toning down the film's on-screen violence. The filmmakers probably considered the depiction of a bloody wound across the neck of a young woman to be too graphic for an otherwise relatively light-hearted movie. I do maintain that this artistic decision lends to some unfortunate confusion, however. Even adding a thin red line across the girl’s neck, with maybe a drop or two of blood, could have clarified things without being too distasteful.

I don't know about that. The statue's head was sliced off cleanly. Certainly appeared to be the result of a razor sharp edge to me.

Plus, the hat would have to be absurdly heavy to break apart stone via blunt force. Sharp edge seems much more logical.