I got a deer in a strange way last season. I had been hunting a fairly large 10pt all season, and was headed down to a bean field to try and find him. On the way down I see two does bedded down, I'm still driving on a lease road and decide that I'll pass them. About this time, the buck with them, that I hadn't seen, gets up, walks 50yds away from me (so, towards me), stops in the two tracks and proceeds to start pawing the ground and and staring me down. At this point I can see that he's mature and a wide spread with good mass, no idea about any points though. I get out of the car, get my gun out of my metal case, put on all my blaze orange, kill the truck, sit there for a while, and decide that its been over 2 minutes, this has got to be legal, shot him in the heart, and he proceeds to paw up the ground furiously. I take another shoot, thinking that I had missed him, and screwed the pooch here. I'd used my door as a rest, and at this point he was slowly trotting, I hit the mirror as I pulled the trigger which put my shot a little further back, the deer kept moving at the same speed. I found him dead 8yds later, just far enough to be out of sight when he went down. At that point I decided that even old white tails can be stupid.
As for mulies being hard, shooting a big mature muley seems hard to me, only time I've seen one within shooting range was on a pheasant hunt. He knelt in the grass, somehow concealed his horns, and our line of guys was no more than 10yds apart, and he slipped through the middle, and exploded out of there after he was about 10yds behind us. Scared some of the guys pretty good, but he looked like he would have been at least a 180" deer.