With the release of the Elemental Evil Player's Companion, there is now a spell that does exactly what you're looking for. Transmute Rock is a 5th level spell available to Wizards and Druids, one of the uses of which is to turn a 40-foot cube of stone into mud.
The Stone Shape spell allows you to, well, shape stone, but only a 5-foot cube at a time. (So I suppose this is an option, just a very slow one.)
The Disintegrate spell can disintegrate stone, but only a 10-foot cube at a time.
The Move Earth spell allows you to alter terrain in up to 40-foot cubes, but only dirt and soft earth, no stone. So if there is a natural cave system, you could remove all the dirt from it, but you can't create rooms in solid stone.
And finally, there is the usual standby. A correctly worded Wish will of course achieve whatever you need it to. (Depending on how nice your DM is.)
However, there is another option: Dominate Monster. An Umber Hulk can burrow freely through solid stone, leaving a tunnel in its wake.
Tunneler. The umber hulk can burrow through solid rock at half its burrowing speed and leaves a 5 foot-wide, 8-foot-high tunnel in its wake.
Conveniently, the Umber Hulk has a Wisdom saving throw bonus of +0, so by the time you can cast Dominate Monster, it should be highly likely to succeed. All you need to do is find an Umber Hulk!
Finding an Umber Hulk could be quite tricky. A Scrying spell will let you look at an Umber Hulk, which in turn will let you cast Locate Creature. However, Locate Creature only has a radius of 1000 feet, so it will require some luck for this strategy to succeed.
An alternative is to use Scrying, then Teleport. This only has a 25% chance of success, unless you Teleport while Scrying, in which case it has a 75% chance of success. Obviously this won't tell you where an Umber Hulk actually is, but having Teleport-ed to one you should be able to Dominate it and then Teleport it and yourself back to the site you wish to excavate.
Another solution, by far the simplest despite me not coming up with it till now, is just to Shapechange into an Umber Hulk and do the digging yourself. Much less risky.
Ulmus Glabra aka Ulmus Glabra Montana is also known as Scotch Elm, Wychwood, Wych Elm, and Witch Hazel. (Witch Hazel is a different shrub in the US). It was used to make divining rods and had other reputed magical properties.
One of the things you lose by just treating components as "junk" and abstracting them away is that it's one of the remaining sources of actually learning something about the real world from D&D, it was one of our favorite things with all the weird stuff in the DMG in First Edition. Don't reject the hold-overs, use them to learn about something other than rolling dice!
Best Answer
A cyst, in the biological sense, is a "closed sac, having a distinct membrane and division compared with the nearby tissue". You would expect to see some sort of membranous, organic sac full of mud, dug into or emerging from the ground.
This possible method of using the clone spell is almost certainly a reference to the depiction of the creation of Saruman's Uruk-hai in Peter Jackson's Lord of the Rings trilogy, which features the new orcs appearing to be grown within grotesque, muddy sacs at the bottom of the mining pits in Isengard - first we see the grown Uruk-hai squirming underneath a membranous cover, then emerge covered in mud as other orcs cut and peel the membrane away, as can be seen in this video or these images:
The game does not describe how you're meant to create or engineer that. The important part, as far as it is concerned, is that whatever magical means are required to arrive at this state, the required resources cost at least 2,000gp - you should assume understanding the spell also conveys understanding of the requirements of an appropriate vessel. However, it is important to remember that the clone spell does not consume the vessel as a material component, so once you have created one horrible fleshy mud-sac you can re-use it to cast clone again if you so desire. One assumes you can shovel in some fresh mud, flesh and diamonds and the membrane will regrow.