It could refer to some poor patient who tried to escape. Maybe his hand was ripped off at the process and just left hanging there.
Wasn't the hand outside the window though? I don't honestly remember which, but I thought it was outside the window.
It makes no difference in any case. Obviously the window is open when patient tries to climb down but could have been shut afterwards.
Or perhaps it's a hand of a nurse like Mephisto is suggesting. Maybe a nurse tried to escape because things went to hell and got her hand ripped off in the process.
The cut seems to be very clean, though. Maybe this is not about ripping after all. Looks more like a work of a buzzsaw or something.
My hypothesis has to be that it was the director who went nuts. Perhaps he was sexually abusing this particular nurse and she threatened to make it public. When danger from the directors part was apparent, she decided to escape through the window. She was, however, caught in act by the crazy director who sawed her hand off in a belief that she would die from blood loss and tell nobody. So it was directors last change to keep her mouth shut.