They Are Essentially Invulnerable
A Zumwalt class destroyer (not a battleship by any means) is faster, better armed, and wind-independent. Speed may come down eventually (not sure what 'low fuel' actually entails) but being independent of the wind and mobile to the tune of say, 10 knots (1/3 the Zumwalt's max listed speed, which is itself probably and undersell) makes it invulnerable-by-proxy. The ship could literally sail such that an enemy approaching it from a single direction would NEVER be able to get a broadside in range. If she's surrounded by foes, then the guns come into play...
You'd probably be engaging with it's main guns. 2 155mm cannon with a range of about 80 nautical miles. It can carry 920 rounds of 155mm ammo. For comparison, your enemies have a range of a couple hundred yards, less if they actually want to hit with a decent amount of shots. a 155 round into any of the brigs, sloops, or even non-pirate ships-of-the-line of "pirate times" would utterly annihilate the wooden sailing ship in question. If you want to save on 155 rounds you engage with your 57mm cannon, capable of over 200 rounds per minute and a range of about 10 miles. Again, this would quite literally reduce any given "pirate ship" to matches in a VERY short amount of time. They're also meant to target ships that are moving at speed, which your sailing ships are def NOT doing. Even assuming a paltry 10% hit ratio that's 92 "pirate ships" sent to the bottom. Except it's worse than that, because a 155 round is so nasty even a near-miss could wreack havoc on something a flimsy as a pirate ship. That's not even counting the guided missiles (ostensibly the ship's main armament) or any personal small arms the crew has. The missiles are gratuitous overkill, and the small-arms, while incapable of sinking a ship, are MORE than capable of rendering the Zumwalt immune to boarders until the ammo gives out.
Then we can talk about the armor. Your average "pirate ship" was maybe a 24-gun ship. Those "guns" would.... not make a dent in the Zumwalt's armor. Even at point-blank hull-to-hull type ranges they're unlikely to do damage. The cannonballs are simply not energetic enough. Maybe, maaaaybe after hours of hammering the same spot you might get something. But of course to do that the attacker would have to get through the 155, the 57mm, the crew's small arms, and somehow magically train every shot for hours on the same 6-inch spot. Even then, the most likely result is "that spot is slightly warm."
The only way a pirate FLEET could take a Zumwalt would be if it was unarmed, dead in the water, and somehow all the doors were unlocked. Because a Zumwalt, unlike a "pirate ship" or anything from the Age of Sail, is designed to fight with 0 crew on deck, and all hatches sealed. So even if pirates magically did make it aboard, the crew could just sit nice and safe inside the Zumwalt until the pirates starved to death. Because it's the Age of Sail and REAL hard to feed people shipboard.
TL/DR even given an infinite number of pirate ships, the zumwalt could kill until it's ammo ran out, not be fired on until its fuel ran out, and even when both are gone the ship/crew would be in 0 danger with even the most basic of security precautions like "seal all hatches."
As a fun aside, if the Zumwalt has no ammo and feels particularly aggressive, it could literally ram its way through pirate ships with essentially 0 consequence, and without there being a real chance of the smaller, frailer, sailing ships being able to dodge.