As you probably already know it is highly unlikely a deer or elk would attack, but in the one in a million chance one would (has happened I know). Then Bear spray or mace which is an irritant would just as likely cause them discomfort and to disengage an attack as it would a bear or person that was attacking. Nother words I don't think they'd like it.
Did Trigger attack and you had to use your bear spray? Sorry, I couldn't resist. I would think it would work on deer or elk but who really knows. As mentioned before, it is an irritant and should effect any animal.
I work with horses for a living and it will and does effect horses . It will not necessarily effect their skin but if sprayed in their face wear it is hitting more sensitive like the membranes around the eyes mouth or nostrils it would work. A few years ago in yellowstone a ranger was attacked by a cow elk around Mommouth springs . She had a calf with her and she charged him and knocked him off his bike. He turned his bear defense on it and it turned the cow away .
Bring them in on a string. I love this term, if you want to be successful on calling in Elk, try not to just sound like the other caller. We all laugh at each other when we are practicing Elk calling at home or while camping. When I first started calling in Elk, I had no idea what i was doing and it's funny how many I could call in. The biggest Bull that I have called in to date was actually my first. I was making cow calls and screwing it up big time. But it's obvious I didn't screw up...