I cannot answer whether this particular person committed a crime or not. Only a court can answer that. I can give you general information about laws involving destruction of mail.
Under 18 USC 1703:
Whoever, being a Postal Service officer or employee, unlawfully secretes, destroys, detains, delays, or opens any letter, postal card, package, bag, or mail entrusted to him or which shall come into his possession, and which was intended to be conveyed by mail, or carried or delivered by any carrier or other employee of the Postal Service, or forwarded through or delivered from any post office or station thereof established by authority of the Postmaster General or the Postal Service, shall be fined under this title or imprisoned not more than five years, or both.
So it would generally be a crime to deliberately destroy or delay mail that was otherwise deliverable.
If a carrier took back mail that should have been delivered, that would probably count as "detaining" or "delaying" that mail. In the case at hand, though, I suppose the carrier might argue that when you refused to sign for the letter, it gave her reason to doubt that the addressee(s) actually lived there, in which case perhaps the mail should not have been delivered after all. So she might say that she took it all back to the post office for further investigation as to where or whether it should be delivered.
Destroying the mail would similarly be illegal. However, based on other information in your question that is now removed, it appears that she did not actually do so. Merely threatening to destroy mail, if the threat is not carried out, does not seem to be a crime under this section. I don't know whether it might be prohibited by some other statute.
Crimes involving mail are normally investigated by the US Postal Inspection Service, not by local police.
Of course, even if the behavior is not a crime, it may still be cause for the postal employee to be fired or otherwise disciplined.