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.