I've used my .257 Ackley for almost 40 years to take dozens of mule and whitetail deer, pronghorn antelope, several bighorn sheep, a mountain caribou, and a 6x6 bull elk. Most, including the sheep, caribou, and elk were one shot kills.
I shot all of those animals with 117 grain Sierra GameKing, 115 grain Nosler Ballistic tip, or Hornady 120 grain HP bullets. The bullets that I recovered from these animals all had a retained weight of 1/2 less than their original weight.
I have not tried the 100 grain Barnes bullets in my .257, but I am a big fan of Barnes bullets in my .300 Weatherby and my .375 RUM. Most of the TSX and TTSX bullets that I have recovered from animals had retained 99-100% of their original weight. A 100 grain Barnes bullet will certainly retain more weight than any 115-120 grain cup and core bullet.
Place your shot well, and you shouldn't have any trouble killing a mule deer with a 100 grain Barnes bullet.