Rabbi Yudel Shain of the Kosher Consumers Union writes:
I’ll try to explain the preferred method of Schechita as follows;
The cut should be made starting at a point of the neck closest to the rear of the animal and furthest from the head. You want to end the cut just below the point that lines up with the ear of the animal. Note: going past the point of the ear may come to the vocal cord area (turbitz) which would invalidate the Schechita.
The spine bone is thicker and wider towards the back of the animal, it becomes narrower and thinner towards the head of the animal. In order for the schoichet not to hit the bone yet cut and sever all of the carotid / jugular veins one makes that type of angle cut, as you can cut deeper at the point that the spine is thinnest thereby severing all arteries.
There is another important reason to make the schechita on an angle is to prevent the artery from closing and having the blood coagulate. An angled cut is much harder to stop the bleeding.
Erev Shabbos Shmos 5765
As the PETA video demonstrates, shochtim at Rubashkin were not careful to do this type of cut.