Kdtyjb

In the Fantastic Beasts and Where to Find Them textbook, we learn that wizards classify creatures as either "beasts" or "beings", where beings are usually defined by intelligence level:

Not until 1811 were definitions found that most of the magical community found acceptable. Grogan Stump, the newly appointed Minister for Magic, decreed that a “being” was “any creature that has sufficient intelligence to understand the laws of the magical community and to bear part of the responsibility in shaping those laws.” Troll representatives were questioned in the absence of goblins and judged not to understand anything that was being said to them; they were therefore classified as “beasts” despite their two-legged gait; merpeople were invited through translators to become “beings” for the first time; fairies, pixies, and gnomes, despite their humanoid appearance, were placed firmly in the “beast” category.
_{Fantastic Beasts and Where to Find Them: Introduction}

And we see that trolls, for instance, are classified as beasts despite some rudimentary language skills:

The troll is a fearsome creature up to twelve feet tall and weighing over a tonne. Notable for its equally prodigious strength and stupidity, the troll is often violent and unpredictable. Trolls originated in Scandinavia but these days they may be found in Britain, Ireland, and other areas of northern Europe. Trolls generally converse in grunts that appear to constitute a crude language, though some have been known to understand and even to speak a few simple human words.
_{Fantastic Beasts and Where to Find Them: "Troll"}

And "crudeness" is also a factor in being/beast classification:

Several highly intelligent creatures are classified as “beasts” because they are incapable of overcoming their own brutal natures. Acromantulas and Manticores are capable of intelligent speech but will attempt to devour any human that goes near them. The sphinx talks only in puzzles and riddles, and is violent when given the wrong answer.
_{Fantastic Beasts and Where to Find Them: Introduction}

However, I don't see giants mentioned anywhere in the book, implying that they're perhaps classified as beings. (We even see centaurs and merpeople in the book, since they're classified as beasts by their own request.)

But trolls and giants... seem rather similar. We can see from Grawp that they're pretty violent and crude, even if they can understand / speak some rudimentary English:

“Anyway, Grawpy,” shouted Hagrid, looking up apprehensively in case of further falling eggs, “I’ve brought some friends ter meet yeh. Remember, I told yeh I might? Remember, when I said I might have ter go on a little trip an’ leave them ter look after yeh fer a bit? Remember that, Grawpy?”

But Grawp merely gave another low roar; it was hard to say whether he was listening to Hagrid or whether he even recognized the sounds Hagrid was making as speech. He had now seized the top of the pine tree and was pulling it toward him, evidently for the simple pleasure of seeing how far it would spring back when he let go.

“Now, Grawpy, don’ do that!” shouted Hagrid. “Tha’s how you ended up pullin’ up the others —”
_{Harry Potter and the Order of the Pheonix, chapter 30: "Grawp"}

Given this, I'd be rather surprised if giants weren't classified as beasts... but I can't find any mention of them in Fantastic Beasts and Where to Find Them.

Do we know if Giants are classified as beasts or beings?

I can't find canon confirmation, but it seems clear that Giants must be Beings.

Grogan Stump, the newly appointed Minister for Magic, decreed that a “being” was “any creature that has sufficient intelligence to understand the laws of the magical community and to bear part of the responsibility in shaping those laws.”

Giants might be among the least intelligent of Beings, but they can certainly speak and communicate effectively with humans. Note that both Dumbledore and Voldemort sent actual envoys to negotiate with the Giants for their support, respecting them as potential allies rather than as dumb beasts to be used.

Also, consider Hagrid. His father apparently actually loved his mother, which would be ... weird (even more than it already is) ... if she was a dumb beast. It seems that she was a person, albeit perhaps a brutish and violent one. Hagrid is certainly a person, and surely not half Beast.

You compare trolls with giants, but the example you use for giants is Grawp, a child by giant standards.

Trolls generally converse in grunts that appear to constitute a crude language, though some have been known to understand and even to speak a few simple human words.

Grawp has already got at least that far, and he's not only young (if I recall correctly) but also foreign (he didn't grow up in Britain, and there's no reason to think his mother taught him English - probably he only started learning after meeting Hagrid) and an anomaly among the other giants (being much smaller than average, he's at least physically different, and it's possible he might be mentally disadvantaged as well). If he's already doing as well as the most intelligent/communicative trolls ever recorded, then you do Giants a disservice by placing them on the same level as trolls.

Think of the troll in HP and the Philosopher's Stone, compared with the giants we know of from elsewhere in the series. The troll is just a monster, a beast to be defeated by force and magic - nobody even thinks of trying to reason with it. Grawp is much more intelligent: Hagrid and Hermione can tell him what to do and (sometimes, at least) he'll obey. His and Hagrid's mother was presumably even more intelligent and less brutish, to have been able to catch the eye of a human. And the Giant community led by Golgomath were persuaded to join Voldemort, by way of gifts and common cause, not simply coerced like beasts.