The upper mantle is where it becomes interesting. This is just thinking out loud though. The upper mantle is where magmas are being formed, and one of the reasons magma is formed is decompression. Usually this happens because of mid ocean spreading or mantle plumes, but removing one side of let's say a cube of rock is also going to decompress it somewhat. This may cause generation of magma. No worries though - I don't see any reason why it should rise to the surface. If anything at all, it's going to fall down through the hole (but not much, see above). Also, decompression may cause release of volatiles or gas, the most common being CO2 and H2O I guess, also H2S or SO2 depends exactly what is down there. Also, the movement of rocks in an area of the Earth that's not ductile anymore but rather brittle (lithosphere) is sure to cause some earthquakes. Are there earthquakes going to be dangerous for anyone? I don't know.

What would this hole look like if you peeked down? My guess that it will be filled with water. If this hole starts at the ocean, then the ocean will just flow inside and fill it. It is possible that some mega waves or tsunamis will accompany it. It will pour down until it either meets the closed rock, or just evaporates. Remember - it's pretty hot down there. It will evaporate and rise, then cool and starts raining down again and you will have a nice convective cell in the upper few kilometers of this hole.

In contrast, if this was not in the ocean but rather on land, groundwater will fill it in. I guess most of the earth has groundwater (maybe except the large deserts, but even there some water exists) that will just flow inside and create a similar convective cell.