A summary of what I've done and what others have said:
1. I want to do a shoulder mount:
a. I don't want to cape the face in the field: Cape it up to where you can get to the last vertebrae connecting to the skull. Cut the connective tissue around the last vertebrae. I think it's mostly on the sides. Twist and crank on the head, making any additional cuts you might have missed until the head comes off. Roll up the cape to the back of the skull, strap the whole thing to the pack.
b. I'm ok caping the face in the field: Cape the hide off the face/skull and only take the skull cap per below.
2. I want a euro mount. Same as above to get the head disconnected from the vertebrae but don't cape it at all, just cut the hide off at the back of the head. Option one is to just take the whole head out like that. Option two is to cut the lower jaw off to save a little weight. I've done that with the last few. Same method as taking the skull off the vertebrae, just look for the connective tissue where the lower jaw connects to the skull, make cuts and then put your foot in its mouth to step on the jaw and crank on the top of the head until it starts to come off. Brute force and cutting get it done pretty quick.
3. I just want the skull cap. Saw the top of the skull off. I used to take it off straight across the top of the eye sockets, but on the last one I angled both front side cuts down toward the nose from the bottom of the eye sockets. It makes a better looking skull cap IMO if you care. Back cut isn't as important, just a straight line across the back then connect the front an back cuts on either side, basically from the back of the eye socket. I normally take a small saw with me but if not, then you come back with one.
I only kill small bulls so I always pack them out upside down (antlers pointing down) with the head high on the pack. I always tie some orange flagging tape in a few areas on the antlers.