The best way to make holes through a displacement is to start with trapezoid brushes, since they have to be four-sided.
Since you already have your cliff made you need to do some trickery to clip them into the prop shape without them being destroyed. (clipping preserves the individual verticies as best as possible, VMing or resizing scales all the verticies)
So you have your cliff:
Clone your cliff piece so you always have your original to make pieces from in the following steps (or in case you mess up). Then clip off the bottom of your cliff where the top of the doorway should be:
Then clone your original into the same place as the one you just clipped, and clip this one where the side of your door needs to be:
Do the same with the other side and you should have a "n" shape with the displacements overlapping at the corners. Select the top one and clip both end at an angle like this:
Clip each of the side pieces so that they match up and then you should have an end result like so:
Then all that's left is to hit sew to tidy up the seams.
