. . . if we treat rape as deserving of the death penalty, what message does this send to women who are raped?

It sends the message that rape is so terrible that they might as well be dead.

The mental health of rape victims after having been raped is directly correlated to their culture's attitudes towards rape. If they are from a culture where rape is considered "a fate worse than death" and rape victims are shunned as "tainted", they do very poorly indeed. If they are from a culture in which rape is considered an assault similar to being punched or slapped or kicked, but that the victim is pretty much the same as they always were (except for a few bruises that will go away with time), they do considerably better.

Certainly rape is a serious crime, but it is better for everyone if we don't lose our sense of proportion.