If some specific cursed items can be destroyed (rather than taking the suggested steps for their removal) depends on the campaign
While randomly cursed items are quirky, randomly cursed magic items' powers are otherwise determined normally, they are otherwise employed normally, and they can otherwise be destroyed just like the normal versions of those magic items. A pearl of power that can only be used by a creature who worships a specific deity remains, at its core, just a pearl of power. (Randomly cursed items are described on pages 272-3 of the Dungeon Master's Guide.)
However, specific cursed items require DM adjudication on an individual basis. For example, the boots of dancing (DMG 272) (30,000 gp; 0 lbs.) says, "Only a remove curse spell enables the wearer to be rid of the boots once their true nature is revealed." What this phrase means exactly is up to the DM, and the DM has several options.
- Destroying the boots of dancing causes them to instantly recreate themselves around the possessor's feet.
- Removing the possessor's feet causes the boots of dancing to appear on the horrified possessor's bloody stumps.
- Attempting to destroy the boots of dancing deals damage to the wearer, but no matter how much damage is dealt to the boots, they always have at least 1 hp remaining.
- The wearer can remove and discard the boots of dancing, but when in a position where the boots would once again activate, the boots reappear on the possessor's feet.
…And countless variations of the above and entirely new options besides.
In the end, it's up to the DM. There's no way of knowing if a specific cursed magic item can just be broken or lit on fire so that its curse is lifted, bypassing the need to get a remove curse or similar effect, without also knowing how the DM intends to handle cursed items in the campaign.