It's a pretty big area back there and razors are very small. It would take decades or maybe evenover a hundred years of regular use before it is likely to fill up. The building could even be condemned or otherwise destroyed before it's full.
But yes, if it did somehow fill up, you would need to remove the tiles and cut a section out of the wall to empty it. That's not so big a deal if you only have to do it every 50+ years.
It just dumps out to the empty space in the wall all the way to the floor, it would take a very very long time to fill that up to where it's "full", you'd have to fill the wall to that height in a wide area near the hole