The meaning of the second sentence can be completely differently from the first.
1. The man is too severely injured to be saved even by a doctor, let alone by a layman like me.
This means that the man can't be saved by a doctor, and certainly not by you, since you aren't a doctor.
2. Even a doctor can't save a man so severely injured, let alone a layman like me.
Depending on how you interpret it, the syntax could mean that even a doctor can't save a man so severely injured, and a doctor certainly wouldn't be able to save you.
Of course, the interpretation of the second sentence I give doesn't follow any logic from the sentence itself; however, the syntax certainly allows it. It would only make sense if laypeople, by definition, were always more than severely injured.