Yes you can at times, it some places.... ..but there are limits on what is possible but like Minecraft... no, never.

https://steamcommunity.com/sharedfiles/filedetails/?id=2776714735

You can do some neat things in the mountains digging under rocks. Sometimes there are so many large stone formations in one place that you can have a pretty decent home dug out of the side of a mountain.

It's a pain, though. You can't always tell exactly how a rock formation will break up, so sometimes trying to make small edits can cause the whole thing to collapse.

only you can do that below The Elder Altar , not in normal terrain

Originally posted by blankitosonic:

only you can do that below The Elder Altar , not in normal terrain

Also below any other rocks. The mountains have a lot of large rock formations which you can undermine, and thereby make caves/underground. However, if you fully undermine these they can collapse (crumble).

Hell it took Minecraft a decade to start generating underground terrain worth exploring, and that had fully 3d dynamic terrain from the very beginning. Mayyybe as a really involved mod years after full release.

Sorry to disappoint, but the devs will not introduce such a functionality. It would require a complete overhaul of the game terrain system.

You can already dig ditches and flatten ground as for tunnels I read somewhere that they said they will not add tunnel digging.

It's not a voxel game (meaning it's not made out of cubes like minecraft). You won't ever be able to dig tunnels in the ground. IN the mountains, there are areas you can dig, but you're pretty much raising or lowering the "ground". There's no way to get under it. it's like a sheet thrown over a bed, with lumps and dips. But under the sheet is... nothing.

The developers would have to completely redesign the terrain into a fully polygonal one, which is de-facto equal to the new game

Unlikely.