He was digging in a valley and just happened to find his axe? Wow! That's pretty lucky, isn't it? No, the translation makes no sense to me, but, of course, I do not know the story from which it came. Nevertheless, here is my translation:抇其谷而得其鈇.“He found his axe whilst digging in the valley.”
Besides meaning "to dig," 抇 (홀) can also mean "to rummage through" or "to ransack." And besides meaning "valley," 谷 (곡) can also mean "deep cave." The cave could have been occupied, maybe by a band of robbers. Or maybe someone threw the axe into a hole-like cave, and the person went down into the hole to retrieve the axe, by "rummaging around the cave." At any rate, which translation makes more sense?抇其谷而得其鈇.“[He] ransacked (抇) the (其) cave (谷) and (而) got (得) the (其) axe (鈇).
Finally, this is just a crazy thought that is bouncing around in my head, so don't take it too seriously: Could the character 谷 (곡) have been used to represent 墓 (묘), which means "grave"? Again, I do not know the story from which the sentence came, so I really have no idea.
UPDATE: Maybe the translation in "Du's Handbook" was correct after all. Below is a translation of a Chinese story about an "Axe." This is another example of my writing before Googling.