Having bowled plenty of deliveries over the years that moved one way in the air and the other off the pitch, apparently I was breaking the laws of physics all this time. Who knew?
When you swing it in the air one way, when it goes off the pitch the other way, it's generally seam movement, due to well... orientation of the seam.
When you drift a ball through rotation one way (regardless of whether you're a medium bowler doing a cutter or a slower spin bowler) the ball coming back the other way is conventional turn/cut from the ball rotation gripping on the pitch.
Neither of these cases are breaking the laws of physics. Now the two opposite cases (swing then cut OR drift then seam) are problematic. A swing ball is bowled with backspin, with the seam slightly angled one way, why the **** would it cut off the pitch when you're not imparting any horizontal spin, so it's pretty safe to assume the movement is off the seam, or a vagary of the pitch (Mcgrath used to do this all the time on the Lords slope with his outswinger going away from the righthander and coming back in from the slight hill grade, with the effect being that of looking like an extremely quick cutter).
The drifting ball seaming in, is similarly problematic, although less important, because the ball coming in off the pitch from the seam usually wouldn't even get as much movement as the turn you could get anyway, so is a less important example, but once again even if you hit the seam on a spin delivery, you're generally trying to get a more predictable and greater effect from the turn.
So for that reason, when we hear about a SWINGING ball cutting off the pitch, it sounds kind of a weird form of terminology, given that most of us will have seen a drifting ball cutting or a swinging ball seaming.