We’re actually not sure about that. Some prions do spread by eating the meat of infected animals, but I think we can be pretty sure that’s not what’s happening in a wild deer population. Prions can also be found in the environment, including deposited on grasses and plants, where that can last a very long time.
We do not know if this disease is or will become communicable to predator animals or what the potential is for environmental spread to livestock. We do know a bit more about the BSE than some others, but there’s a bunch we know exist that we know little to nothing about, and it’s guaranteed there’s more out there that we haven’t encountered yet.