The US / common law jurisdictions typically only have very light self-incrimination protections. The 5th amendment in the US only protects against self-incriminating testimonial. That's it.

In most other jurisdictions (i.e. civil law) it's perfectly legal for the accused to destroy evidence (assuming you're not committing any other crimes in doing so, like breaking and entering, property crime etc.), seizure being ordered or not, while it remains illegal to destroy evidence at the behest of someone else. I.e. civil law usually doesn't criminalize self-protective conduct. That's true even in e.g. Japan.