Slingshot for deer, doubt it
If I were in a totally survival situation and had to kill a deer, I would forget about physically hunting for it. I would set snares that would work 24/7 along good game trails.
Please understand that doing so is TOTALLY ILLEGAL, but we are talking a hypothetical situation.
Yes, I do know how to set snares for large and small animals. I have snare materials in some of my preps.
To answer the OP question about killing deer with a slingshot, I guess it could be done, but IMHO, VERY unlikely and inhumane. I agree that "if" you could hit the deer, you are more likely to only cause an injury to that animal. Would it cause the deer to go off and die elsewhere? That all depends on where and how you hit it and with what projectile.
Personally, I would not even attempt it. Again, if I was in a survival situation and my life depended on my getting a deer to feed my family and myself, snares is how I would do it and I'd set more than one to increase my odds well over what someone with a slingshot has of killing a deer.
Jus sayin
Medic73