Based on what Bird has said about the phrase "The Lord sure do work in mysterious ways" coming from the Gary Cooper movie and based on Nat's saying that the current owner painted this on the tractor, I suspect Sgt. Cooper didn't say this about himself. I think it is an observation made through the movie about Sgt. York's remarkable life.
As I was reading about Sgt. York, he was described as being under strong religious conviction about not killing and was apparently going to be a conscientious and religious objector to his being drafted for WWI until he found a verse that he believed permitted him to serve as a soldier.
York is credited with "taking 32
machine guns, killing 28 German soldiers and capturing 132 others" largely by himself because the surviving members of his small unit were pinned down. York would have been using a bolt action rifle with about a 5 shot magazine and a Colt .45 autoloading pistol. In reading the book, it is plainly evident that York gave credit to God for his own survival. And in his later life, it is evident that he turned away quite a bit of money for his "story" because of his convictions.
So in the context of what happened in Sgt. York's life and how he lived, I can now understand why the owner of the tractor would deem it appropriate to paint this phrase summing up Sgt. York's life on Sgt. York's tractor.