Yes, motorised ones can drag your arm in before you get a chance to knock the 'off' switch. When I was a child we had one, briefly, luckily no accidents in our household, but the reports of nasty injuries were enough to make my parents get rid of it.
There was a hand-operated mangle at the school swimming pool for wet swimsuits. After a few pinched finger incidents, it became the rule that the handle had to be operated by the person feeding in the wet swimming cossie!