in pugilism, a close-in strike upward with the fist, 1831, from upper + cut (n.). Perhaps the image is of chopping a tree by making cuts up (as well as down) in the trunk.
It was on a side hill, and I observed a boy, who appeared to be about fifteen years of age, opposite the house felling a large tree; he had cut a few chips from the under side, and was then making the principal incision on the upper. ... I said to the boy, "Well Sir, I see that you make the upper cut." "That is the true cut," said the boy; "for if you will take the axe and try below, you will find that the tree will crowd down upon your chips, and you can't get it down in double the time." [Theodore Sedgwick, "Hints to My Countrymen," 1826]