a 357 mag will most certenly kill a deer but as stated you have little wiggle room, and have to watch what bullets used and range.

deer are not overly tough animals to kill an you could kill one with a 22 long rifle but it wouldnt be my first chioce.

If you can try and go up in bullet size try a 41 magnum or a 44 special. bigger bullets that expand make bigger holes in the deer and more blood