Texan Red Deer are 5th grade girls compared to some of the things I've seen shot. A well placed shot with just about any caliber will DRT em. I shot my hind with 22-250 Remington 55gr PSP at 80yd in the neck. That deer did not move except towards the dirt-ridden ground. My uncle shot a 4 yr old stag tight behind the shoulder (armpit) with 150gr 270 Corelockt PSP at about 60yd and that thing literally flipped over and died.
Recently, a friend of mine shot a really, really nice stag with 30-06. Less than 50yd blood trail. And on the same ranch, a different hunter shot a huge hind with the 270. Same short recovery.
Good luck on your hunt.