Harry almost killed Malfoy in Harry Potter and the Half-Blood Prince, with it. The next year, George lost an ear due to Snape. These facts, and the "For Enemies" note should clinch it.
Not many people knew Sectumsempra - they'd need to know it exists to ban it.
Severus Snape invented Sectumsempra while at Hogwarts, and wrote it down in his Potions book. He doesn't seem to have told many people about it, it's possible he didn't tell anyone at all.
“Harry was about to put his book away again when he noticed the corner of a page folded down; turning to it, he saw the Sectumsempra spell, captioned ‘For Enemies’, that he had marked a few weeks previously.” - Harry Potter and the Half-Blood Prince, Chapter 24 (Sectumsempra)
His book was hidden away until Harry found it, and Harry didn't tell the rest of the wizarding world about it either. Severus himself was seen using Sectumsempra when the Order was moving seven Harrys, and Harry had used it a few times after he found it in Snape's old book. Lupin knows of it, since he described it as one of Snape's specialties.
However, they are probably some of the only people who know it - it isn't widely known like the three Unforgivable Curses. No one else, either in the Death Eaters or the Order of the Phoenix, is ever said to use it. It's likely that the Ministry didn't even know of it. Therefore, the Ministry wouldn't have even been able to make the decision to classify it as an Unforgivable Curse, since they would likely not have even known it existed.
If the Ministry knew about it, would it be classified as Unforgivable?
The reason it wasn't classified as an Unforgivable Curse is because the Ministry wouldn't have known about it - they would be unable to make any decision on something they don't know exists. That, by itself, doesn't say whether the Ministry would classify it as one if they knew about it.
Not all potentially harmful spells are classified as Unforgivable Curses.
It's nowhere near guaranteed, though, that if the Ministry knew about Sectumsempra, that they'd classify it as an Unforgivable Curse. There are other spells that could clearly do harm. Just to give a few examples - Confringo, Flagrante, and the creation of Fiendfyre are all potentially harmful but not Unforgivable.
It's never mentioned why those three curses are classified as Unforgivable and others aren't, but it seems likely that it's because there are little to no uses for them that aren't evil. The punishment for using an Unforgivable Curse is a lifetime sentence in Azkaban, so only the worst curses, that are highly unlikely to ever have a non-Dark use, would be made Unforgivable.
“Now … those three curses – Avada Kedavra, Imperius and Cruciatus – are known as the Unforgivable Curses. The use of any one of them on a fellow human being is enough to earn a life sentence in Azkaban.” - Harry Potter and the Goblet of Fire, Chapter 14 (The Unforgivable Curses)
Now, would Sectumsempra fit the criteria for being made an Unforgivable Curse?
Probably not - it cuts through things like a sword. It can be used for anything a sword, knife or other cutting tool can be used for. While using it on people might be considered Unforgivable, the spell itself is simply the act of cutting. There are many things a wizard might reasonably want to cut with no malicious intent; vegetables, rope, cloth, building materials. Because of this, it seems unlikely that even if the Ministry had known about it, it would be classified as an Unforgivable Curse.
In addition, there is a countercurse for Sectumsempra.
“Pushing Harry roughly aside, he knelt over Malfoy, drew his wand and traced it over the deep wounds Harry’s curse had made, muttering an incantation that sounded almost like song. The flow of blood seemed to ease; Snape wiped the residue from Malfoy’s face and repeated his spell. Now the wounds seemed to be knitting. - Harry Potter and the Half-Blood Prince, Chapter 24 (Sectumsempra)
While the wounds from Sectumsempra can't be healed by simple healing spells, they can in fact be healed by the countercurse.
So - Sectumsempra likely wouldn't be made Unforgivable if the Ministry knew it.
It isn't Unforgivable in the way that the Unforgivables are
A popular fan theory is that there is no grey area with Unforgivable curses. They do what they say on the tin and nothing else. Killing curse kills, imperio controls, crucio tortures. The caster also has to fully understand and mean to cause the effect the curse entails too. There's no excuse for fully casting them other than they wanted to kill/control/torture.
This is alluded to in OotP when Bellatrix taunts Harry about his weak/failed Crucio:
Hatred rose in Harry such as he had never known before: he flung himself out from behind the fountain and bellowed, "Crucio!"
Bellatrix screamed: the spell had knocked her off her feet, but she did not writhe and shriek with pain as Neville had – she was already back on her feet, breathless, no longer laughing. [...]
"Never used an Unforgivable Curse before, have you, boy?" she yelled. She had abandoned her baby voice now. "You need to mean them, Potter! You need to really want to cause pain – to enjoy it – righteous anger won't hurt me for long – I'll show you how it is done, shall I? I'll give you a lesson —" (36.30-32) Order of the Phoenix
And again with fake!Moody in the Goblet of Fire where he claims during the Unforgivables class that if the class were to all point their wands at him and say "Avada Kedavra" he wouldn't get much more than a bloody nose - they'd have to mean it for him to die
"Avada Kedavra's a curse that needs a powerful bit of magic behind it — you could all get your wands out and point them at me and say the words, and I doubt I'd get so much as a nosebleed"
Sectumsempra is different:
Harry is able to fully cast Sectumsempra off-hand and in a panic without understanding any of it's effects. Plus the curse is ambiguous as to how much damage it does, and as Snape proves the damage is reversible. This makes it on par with spells like Reducto, Confringo, or Bombarda Maxima. Each of these spells could be used to decimate another wizard, but also could be used to wound instead.
I would imagine in the HP universe there are more than just three curses that you aren't allowed to use too - the Unforgivables are just the worst and so are on another level. Sectumsempra would most likely regarded as Dark/illegal/restricted, along with other spells such as the organ-expelling/skin-boiling curse etc.
Since only Snape and Harry ever cast it, the Ministry doesn't really need to be concerned
Severus Snape invented Sectumsempra. When Harry tried to cast it on Snape, he said:
"You dare use my own spells against me, Potter? It was I who invented them ~ I, the Half-Blood Prince!"
—Harry Potter and the Half Blood Prince
Let's assume that Snape is telling the truth on this and that he did indeed create it. The only two people we see cast it are him (Lupin said that Snape was the one who cut off George Weasley's ear at the Battle of Hogwarts) and Harry (who vows never to use it again).
Snape is at this point is a known Death Eater and there isn't much point in criminalizing a spell that only he is casting. And the Ministry seems unaware that Harry committed it.
But if the Ministry starts getting hundreds of reports that non-Deatheaters were casting it, they might have decided to make it an Unforgivable Curse.
Sectumsempra could have forgivable uses
In Why isn't the Memory Charm (Obliviate) an Unforgivable Curse?, the highest answers note that despite a potential for horrific abuse, the Ministry uses the Memory Charm regularly for accepted, legitimate uses. However, the Unforgivable Curses like Cruciatus are assumed to not have legitimate uses.
It's possible that there could be a case where "slashing like an invisible sword" could be useful. Perhaps it could be used for cutting down trees, or for medical amputation, or for slaughtering farm animals. If any of these are seen as reasonable uses for the curse, then there are circumstances where casting Sectumsempra may be forgivable.
Curses just as bad aren't Unforgivable
Heck, if we're following the movies, the Blow People Up Into a Million Pieces Curse is arguably worse than Avada Kedavra, but it's perfectly okay for Molly Weasley to do it.
Because at most two or three people seemed to know about it.
The spell literally only appears on people tightly related to Snape. The only reason Harry knew the spell is because he ended up with Snape's old textbook with the notes in it.
It's not like the Ministry of Magic has enough time or competency to run down every possible combination of dark magic, and draft particular laws against each. They'd have to be adept at researching and doing dark magic and find unknown spells to begin with, which is ground very few are willing to tread.
The Unforgivable Curse laws covered the three most well known spells, and with those three the most common goals of those following the dark arts - domination, control, and death. Anything else they probably have a more generic law for. "Magic with intent to murder" ought to cover it, which would cover anything from Sectumsempra to levitating an anvil.
What is an unforgivable curse?
From what we know of them, the unforgivable curses all need to meet all the following conditions:
- They require full intent
- They are meant solely to cause harm
- There is no countercurse
- The intended harm cannot be reversed (Death, pain, control/action by proxy)
- They are primeval spells (meaning they were invented before the formalization of magic, spells and the civilised magical world).
As can quickly be seen, sectumsempra fails at least 3 of these. It is not an unforgivable curse.