For a deer as large as the mule deer, I would try to find something in a 180 grain load that the gun likes.
There isn't a mule deer alive that any .30-06 cup and core 150 grain hunting bullet from any of the major ammunition companies wouldn't kill, when placed properly placed. Find one that your rifle likes, put it just behind the deer's shoulder, and enjoy your venison. Don't over think it.
