Political Power / Charisma / Psionics
I know this probably is far afield of what you had in mind, but it strongly bears mentioning, especially in fantasy settings. If you're a <PERSON> or another type of ruler, you need neither technology nor magic if you have enough strong bodies who are either willing or forced to do the hard manual labor.
This can be accomplished directly by Political Power, or directly/indirectly by Charisma or Psionics.
Let's take Psionics first. Some might argue this is "magic" but if the author postulates that it is, in fact, a biological or physical trait, then it's a question of which way the reader chooses to perceive it. Psionics might be used directly: "Hey, wouldn't it be a good idea for you and all your buddies to go dig out and level that mountain?" But you'd have to do this to a LOT of people.
Psionics could also be used to achieve Political Power, which might be more convoluted, but is probably more efficient in the longer term. You can imagine how someone could [mis]use such a capability to become politically powerful.
Next, consider Charisma. The strongly charismatic character can often convince others that actions they'd normally never consider are, in fact, a good idea. 805
This works almost the same way as Psionics except that it isn't metaphysical, and the recipient is at least a partially-willing participant.
Thus the same arguments hold for Charisma: our (Machiavellian) character is probably better off using it to achieve political power first. Otherwise you have to talk to and convince a LOT of people.
Which brings us back to Political Power.
* If you are a dictator, you can simply order your subordinates to plan and execute the removal of the mountain by whatever means necessary. You need not even concern yourself with how they'll accomplish it, though their solution (in a primitive setting) likely involves conscription or outright slavery.
* If you are a person of lesser power within the organization of a dictator or monarch, you need to earn brownie points with your allies -- and collect dirt on your enemies -- so that both groups cooperate with you when you propose your plan to the leader. If you're a GREAT manipulator, you maneuver others into deciding to do your idea(s) for you. This is even more effective, because if anything goes wrong with the plan, you were the person saying it was a bad idea all along, and others end up taking the blame.
* If you are a duly elected official, you will still use such sneaky and underhanded --- sorry, I mean cleverly bipartisan --- means to build your power base and accomplish the goal of flattening the mountain. This might be a lot more difficult than the other two possibilities because you also must find the funding to pay the workers who will be hired to do the physical labor!
Use of Political Power can become very ugly, very quickly. But it can get things done that were otherwise not possible. 164