I have killed 2 mule deer bucks now with .223 rem. In Utah.
One shot kill with saiga .223 on a medium 3 point buck at 100yds. .55grain soft point Bullet went through both lungs and the heart, then exited the other side, deer made it less than 10 yds.
Second one was with RRA 24" varmint, .64grain soft point .223 at about 200yds, another medium size 3 point buck. Hit him a little far back, in the guts, and it droped him, he was trying to drag himself away with his front legs, when the next one got him in the neck, and it was all over, again less than 10yds.
With the shot placements I made, I dont think that any other cartrige would do any better, also there was no ruined meat on either one.
I have shot other mule deer with 30-06, 7mm rem mag, 30-30 win, 7mm08, and 308. The .223 is not the best choice, but it will work.