Seems to me that you need to cut off a total of 1 1/2 inches in 2 adjacent sides to make the 15" a 13 1/2" right?
That would mean that you have to either cut 3/4 of an inch off all four sides, or 1 1/2" on two adjacent sides.
Am I thinking right?
Put the square up on to block and just pin where you think you need to cut before you do the actual cutting and measure. That should tell you if your right before making a mistake.