That's how the whole problem with mad cow disease got started. They feed on grass and other herbage.
Cattle eat meat naturally, too.
BSE is an incurable disease caused by a mystery 'infectious agent'. The agent is not a virus or bacteria - nobody knows what it is. It has broken the most basic rules of biology. Any cure still lies at the very limits of present-day science. That is why it is illegal in the U.S. to give feed made of dead livestock to cattle.