Short answer. Yes, if your jewel is much more precious than the item it's set into. Article 469 of the Civil Code lets the owner of the more valuable accessory thing demand its separation even though the principal thing it was incorporated into may suffer some injury, so long as the accessory is much more precious than the principal.
What the law says
in case the thing united for the use, embellishment or perfection of the other, is much more precious than the principal thing, the owner of the former may demand its separation, even though the thing to which it has been incorporated may suffer some injury
Civil Code, Article 469 — Separation of United Things. Read the full provision →
What the law says
Whenever the things united can be separated without injury, their respective owners may demand their separation.
Civil Code, Article 469 — Separation of United Things. Read the full provision →
Separation is allowed even with injury, if much more precious
Article 469 provides that in case the thing united for the use, embellishment or perfection of the other, is much more precious than the principal thing, the owner of the former may demand its separation, even though the thing to which it has been incorporated may suffer some injury. A jewel set into a cheaper item for its embellishment fits this description if the jewel is genuinely much more precious than the item — you can demand separation even at the cost of some damage to the item.
The general rule this exception builds on
The article opens with the ordinary rule: whenever the things united can be separated without injury, their respective owners may demand their separation. Where separation is possible without hurting either object, each owner can simply demand it back, no comparison of value needed. The much-more-precious exception only becomes necessary because your situation involves removal that would injure the cheaper item — otherwise the general rule alone would already let you demand your jewel back.
Why value, not fault, is the deciding factor
The article does not ask who caused the two things to be united, or whether the setting was done with your consent — it focuses on the relative value of the accessory versus the principal thing. Being much more precious is the threshold the article sets: a jewel of only slightly greater value than the item it is set into would not obviously meet this standard, even though it would still belong to you.
What the article does not resolve
Article 469 establishes that separation can be demanded despite injury to the principal thing, but it does not itself define exactly how much more precious the accessory needs to be, or address compensation owed to the owner of the item that gets damaged in the process. Those questions depend on other provisions and on the specific facts of how much your jewel is actually worth compared to the item it was set into.