She cut her finger cutting an apple.

Not natural, since the finger isn't cutting an apple.
Natural: "She cut her finger while cutting an apple."

Mr. TomShe cut her finger cutting an apple.

Hmmm. For me, this is quite acceptable. I would never read it as implying that her finger was cutting an apple. (To be very fussy, I do notice the repetition of "cut". If a different verb could be used in either place then that would be stylistically better.)

Yes, perhaps "She sliced her finger cutting an apple."
However, I would be adding context that was unknown.

I think it's more likely that it was the apple that was sliced than the finger.

fivejedjonI think it's more likely that it was the apple that was sliced than the finger.

Obviously, you haven't seen me in the kitchen.

Thanks!

…however it is quite interesting to note that such a small sentence can have such variegated responses from different native speakers.

Tom

PS: I cut myself shaving or I cut myself while shaving.