It is quite simple: Sauron did not expect, and could not conceive, anyone would actually try to destroy the Ring instead of claiming it for themselves.
"
He is in great fear, not knowing what mighty one may suddenly appear, wielding the Ring, and assailing him with war, seeking to cast him down and take his place.
That we should wish to cast him down and have no one in his place is not a thought that occurs to his mind.
That we should try to destroy the Ring itself has not yet entered into his darkest dream.
"
- The Two Towers , "The White Rider" This complete lack of desire of any kind to master the Ring was the primary reason Frodo was chosen to be the Ringbearer.
Even Gandalf refused to touch the Ring for fear of being consumed by it and not being able to destroy it.
Edit:
During a re-read of The Fellowship of the Ring
I have come across these other relevant passages:
Well, let folly be our cloak, a veil before the eyes of the Enemy!
For he is very wise, and weighs all things to a nicety in the scales of his malice.
But the only measure that he knows is desire, desire for power; and so he judges all hearts.
Into his heart the thought will not enter that any will refuse it, that having the Ring we may seek to destroy it.
If we seek this, we shall put him out of reckoning.
And this account from Isildur who could not even bring himself to put the ring in a fire:
The Ring misseth, maybe, the heat of Sauron's hand, which was black and yet burned like fire, and so Gil-galad was destroyed; and maybe were the gold made hot again, the writing would be refreshed.
But for my part I will risk no hurt to this thing : of all the works of Sauron the only fair.
It is precious to me, though I buy it with great pain.
Both excerpts from The Fellowship of the Ring: Book II:
Chapter 2: The Council of Elrond .
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This was a key point of Gandalf and Aragorn's strategy, and the whole reason they led the army of Minas Tirith to the Black Gate of Mordor.
The hope was to draw not only Sauron's attention, but his armies as well, leaving Mordor itself unguarded.
Book 5, ch. 9: [Gandalf]
: ‘His doubt will be grow­ing, even as we speak here.
His Eye is now strain­ing
to­wards us, blind al­most to all else that is mov­ing.
So we must keep it.
Therein lies all our hope.
This, then, is my coun­sel.
We have not the Ring.
In wis­dom or great folly it has been sent away to be de­stroyed, lest it de­stroy us.
With­out it we can­not by force de­feat his force.
But we must at all costs keep his Eye from his true peril.
We can­not achieve vic­tory by arms, but by arms we can give the Ring-bearer his only chance, frail though it be.
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In addition to all the other comments, guarding Mount Doom is difficult.
It regularly erupts, so having soldiers on guard duty near to it presumably raises the very real risk of them being burnt to a cinder.
The road to Mount Doom had to be regularly cleared and maintained at great effort according to the books, so the most likely group of Saurons servants you were likely to find there would probably be a highway repair crew...
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Mordor itself was actually heavily guarded, with legions of Orc troops occupying it, as we learn in The Land of Shadow : Frodo and Sam gazed out in mingled loathing and wonder on this hateful land.
Between them and the smoking mountain, and about it north and south, all seemed ruinous and dead, a desert burned and choked.
They wondered how the Lord of this realm maintained and fed his slaves and his armies.
Yet armies he had.
As far as their eyes could reach, along the skirts of the Morgai and away southward, there were camps, some of tents, some ordered like small towns.
The fact is that Frodo and Sam had taken a little-known back-door into Mordor; the main entrance (via the Black Gate) was effectively impassable (from
The Black Gate is Closed ): Across the mouth of the pass, from cliff to cliff, the Dark Lord had built a rampart of stone.
In it there was a single gate of iron, and upon its battlement sentinels paced unceasingly.
Beneath the hills on either side the rock was bored into a hundred caves and maggot-holes: there a host of orcs lurked, ready at a signal to issue forth like black ants going to war.
None could pass the Teeth of Mordor and not feel their bite, unless they were summoned by Sauron, or knew the secret passwords that would open the Morannon, the black gate of his land.
And even the back-entrance they took was also well-guarded ( The Tower of Cirith Ungol ):
Since his return to Mordor, Sauron had found it useful; for he had few servants but many slaves of fear, and still its chief purpose as of old was to prevent escape from Mordor.
Though if an enemy were so rash as to try to enter that land secretly, then it was also a last unsleeping guard against any that might pass the vigilance of Morgul and of Shelob.
In order to actually do anything useful at Mount Doom, you obviously have to get into Mordor first, which is something that one does not simply do.
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Recall that that was why the host of men challenged Sauron in open battle, knowing full well that Sauron is too greedy to not want to commit his forces to defeating Isildur's heir.
This led Sauron to take the bait by emptying his land to fight Aragorn and the armies of men.
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Sauron believed not only that no one would want to destroy the Ring, but that no one could destroy it.
That is, that no one could summon the willpower to destroy the Ring at the very Cracks of Doom where it was created and where it would be at its greatest power; and he was right.
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This fact had always bugged me. When Frodo finally goes to the Cracks of Doom he is met with practically no resistance. This seems uncharacteristic of Sauron which in my humble opinion makes it a tiny flaw in the plot. Just to be safe, Sauron could have heavily guarded Mount Doom to prevent the destruction of the Ring: why didn't he do so?
Why didn't Sauron guard Mount Doom?
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<the-lord-of-the-rings><tolkiens-legendarium><sauron>
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scifi.stackexchange.com/users/28152/Ram G Athreya
Sauron did not expect that anyone would try to destroy the Ring instead of claiming it for themselves.  He also believed that no one could  destroy it. Simply put, Sauron believes that nobody would want to or would be capable of destroying the ring and so does not feel compelled to guard Mount Doom.
Sauron believes that nobody would want to or would be capable of destroying the ring.