We are instructed not to separate what He has joined together. We are not told it is impossible for us to separate it. Rather, the fact that we are told not to shows that we can separate it - and therefore need to be told not to.
Which also means that, once separated, although the separation may not have been His will, it is still real.
It is interesting to me that marrying a divorced woman is still considered adultery, as if the marriage still existed. It is as if a woman getting a divorce does nothing.