The claim of general relativity is that a black hole is a singularity in spacetime, meaning that space effectively "ends" there. A very crude model would be cutting a hole out of fabric and then sewing the circle up into a point. The area of the hole is "gone" --- it's not like it's there and you can't see it, it's just not there. I guess that it is what you mean by "devoid of space".

Then the rest of the fabric is bent in weird ways around the fact that there's a chunk missing, which in physics manifests as as everything being pulled towards it (and there is a point, the event horizon, at which things are no longer possible to interact with, like you're too deep in the hole to get out again.