The only way to kill a deer with a 357 is a head shot. I have shot 2 deer (notice I didn't say killed), they both just walked off. The 1st deer I did knock down 2 times and it still ran off and I found it 3 hours later approx. 1/4 mile away.
The 2nd just stood there after being hit in the neck 6 feet from my stand. The bullets did not exit either deer. I picked up the 30-06 and killed it.
It's just not enough to do the job. I would start with at least a 41 magnum. hpg