"You can discard 1 card; negate the activation, and IF YOU DO, destroy it".
The destruction is not 100% guaranteed, since if Dark Cavalry's effect is negated, the destruction will not happen.
Stardust's effect can not be chained to an effect like that.
Stardust can't respond only if the destruction wasn't the last thing to happen, or if the destruction involves uncertain element as cost, like dice roll or coin toss.
If being able to be negated means Stardust can't respond to it, then Stardust won't be able to respond to anything at all, as every single destruction effect can be negated.
Besides, if Dark Cavalry's effect is already negated, why would he still need to use Stardust to negate the destruction? I assume this means Dark Cavalry's effect was not negated, and something else is causing him to be unable to respond.
For example, was that Stardust Dragon summoned using Necroid Synchro? Necroid Synchro negates the "Stardust" monster's effect.
The Stardust Dragon was summoned using Stardust assault warrior and a lvl 2 tuner, so a normal synchro. I then activate a spell which Dark Cavalry negates and destroys but SD wasn’t able to negate.
I'm confused then, either you missed something else, or it's a "bug", in the sense that they forgot to account for this card's interaction with Stardust. If you still have the replay, try reporting it.
It's not a bug, Stardust triggers off purely destruction effects- not effects that first negate then destroy the card if they do. It's the same reason why Stardust isn't able to negate counter traps, look it up
...Stardust Dragon can't negate Counter Traps because it's Spell Speed 2, and thus can't be chained to ANY Counter Trap.
The reason Stardust Dragon can't negate Dark Cavalry in that scenario is because when the activation of a Spell/Trap Card is negated, it's not considered to be on the field, and Stardust can only negate effects that will destroy a card on the field.
If Dark Cavalry was instead negating the activation of the effect of a card like Blaze Accelerator or Black Rose Dragon, you could use Stardust Dragon to negate it.