In Princes of the Apocalypse, a player got hit with Ghaunadaur’s curse... The rules for the curse state (Temple of the Elder Elemental Eye, room F19; PotA, p. 121):

The curse is like a polymorph spell, except it turns the offender into an ochre jelly that lacks the Split reaction. A greater restoration or remove curse spell ends this effect.

It says it's like a polymorph spell... and polymorph's description says that:

The transformation lasts for the duration, or until the target drops to 0 hit points or dies.

The part I'm hung up on is the a greater restoration or remove curse spell ends this effect part... does that mean only a greater restoration or remove curse spell ends the effect? The wording almost suggests that this overrules the way polymorph works (since it's a curse).

Bottom line - does dropping to 0 hp end the curse?

By RAW, yes, dropping to 0 hp does end the curse

If the text you gave is, as stated in your comment, the only information given about the curse, then all the normal means of ending a polymorph spell will end the curse.

As quoted,

The curse is like a polymorph spell, except it turns the offender into an ochre jelly that lacks the Split reaction.

Meaning, that it should otherwise be like the Polymorph spell in every way except those that are specifically noted.

A greater restoration or remove curse spell ends this effect.

This doesn't exclude the normal means of ending the spell. It just adds an additional means to end the curse. It still maintains its "like a polymorph spell" status.

To add clarity, you can look at T.J.L.'s answer on this question. To summarize in his words, it's "Additive, Not Exclusive".

No, it is not the spell polymorph

We don't know what "like the polymorph spell" means, but we do know that there are times when a specific mechanic is provided and when something similar is done.

There are many examples of creatures that can "polymorph" but that don't directly associate with the polymorph spell. When that direct mechanic is used, WoTC typically uses language like "as if casting polymorph" with the associated italics. Without the italics and language, I don't think we can assume that it works exactly the same way - especially when there is language on how to remove it that is different from polymorph.

With this curse, we don't know the extent of what the similarity is (other than changing your form and statistics), but we do know that unlike polymorph, the only way to end this is the language in the curse of:

A greater restoration or remove curse spell ends this effect.

That above language is not in the actual spell polymorph, so those are the only things that can end this particular curse and not the standard ways of ending polymorph like HP to 0 or even dispel magic.

Bestowing a Curse

The spell Bestow Curse utilizes similar removal techniques to this particular curse. The listed removal techniques for this spell are Remove Curse and Greater Restoration's specific bullet point. However, Dispel Magic seems to remain an option for Bestow Curse where it is may not be an option for this particular curse. That's up to another question to resolve :)

For whether or not Dispel Magic would work on this curse requires determining if Ghaundaur's Curse is a magical effect or not. Based on this question it does appear that it is a magical effect as it is like a spell.