Hi David
"Does a die cut both ways?" – in my experience yes – but – I'm given to understand that the die should be used with the side with the information marked on leading, as the entrance to the die is chamfered to some extent to help with starting the cut. Using the die the other way round you haven't got this lead-in so you're trying to cut full depth right from the outset. I've got a chipped M12 die that tesitifies to this!
Now the other bit of the "but". On one job I that did, I needed to thread as close to a shoulder as I could, as the length of thread was only about 3 turns maximum, and I didn't want to extend the thread any more than I had to for aesthetic reasons as well as avoiding the shaft end projecting beyond the rest of the finished apparatus. This short thread length was quite adequate, as what was being screwed on was a flange to stop a hand wheel coming off the end of the shaft with the thread, and as everything was "handraulically" operated there were no large forces. Using the die the normal way round left only just over 2 turns engagement for the flange, but by reversing the die and following down the already cut thread I was able to extend the thread to very nearly the shoulder and got the best part of an extra turn engaged. The flange then just needed a small countersink to allow it to snug right up to the shoulder. The result was a much more secure fastening.
So yes in my experience they will cut both ways but it isn't necessarily recommended.
Keith