Yes, this is normal. Not everyone does it to this extent, but it is a normal practice.
The Gophers usually cut backside DL on outside zone plays. Mason's teams did the same. It prevents backside pursuit and allows a runner to focus on where he is going, as well as potentially open cutback lanes.
The picture you posted is from a 3-step drop. Since 3-step passes are quick and the WRs don't get that far down upfield, the QB wants to get a full view of what is happening in the defensive secondary. By cutting, the OL forces the DL to put their hands down, thus opening up the view for the QB. An added bonus to this is that it slows down the DL by giving them one more thing to think about. They can typically do this on 3-step drops because the ball will be thrown before the DL get back up. Again, cutting on pass plays is a fairly standard practice, though it is by no means a hard and fast rule and typically happens more on run plays.
Where you will see cutting the most is by triple option teams (Air Force, Navy, Georgia Tech, etc.). They cut on nearly every play as a part of their scheme. They line up with HUGE splits between the OL and cut as a way of getting across the gap. There are fairly strict blocking assignments (as opposed to the zone blocking we see a lot of here), and cutting is a way of quickly covering a lot of ground and taking out a man that otherwise could not be blocked.
As for Amaefula, my opinion as a coach is that the guy getting cut is to blame for any injury. He needs to protect himself. DL and LBs work constantly on defeating cut blocks because they happen so frequently. My honest guess is that Amaefula will get an earful in the film room about using his hands better.
So, a more succinct answer to your question is that yes, this is a usual practice.