Generally, if your block has parallel sides you can just use to push a hole through the geometry.
However, if the sides arent parallel youd have to extrude the shape you want to cut through the slab then move it in to position, select the whole thing->right click->intersect with selected.
As you said, all this needs to happen with ungrouped geometry (or geometry all in the same group) for it to work.
Itd be useful if you could post a model showing your problem btw, hard to say exactly what the problem is without an example.