Well, that's more the way the sentence is set up, the "Ich habe mir...". That sounds a bit like "I've cut my finger". You'd say "Ich habe meinen Kuchen geschnitten".
But who knows, Austrians are weird. Maybe they have that as a slang word.
Yea! It was weird!
Because then everyone was like "Well how would you say it?"
And she said "I'd just say 'Ich habe ihn geschnitten."
And then we were like "I thought we were supposed to be using the reflexive"
And then she was like "Moving on"
1.) I'm from the most western part of austria, been living in the southeast, where I studied human anatomy, for almost ten years now and I dare saying that I banged my way through every other Bundesland we have. Never have I heard of a body part called "Kuchen".
2.) IMO even "den Kuchen schneiden" sounds odd. "Anschneiden", yeah - but simply "Kuchen schneiden"? :/