Can a husband throw away his separated or divorced wife's mail?
You would need to change the address of the mail you are receiving, or get a Post Office box that your husband has no access to. Then file to have your mail forwarded to the new address. If you get a post office box, make sure that he has no access to it. If he is not living with you, file a complaint that he is stealing from your mail box. You can get a restraining order. If you are still living together, then he has legal access to the mail box.
The Postal carrier is required to put the mail in the box for the address to which it is being delivered. Once you have a different address or post office box, then they can deliver the mail to the new address.
The Postal carrier cannot prevent anyone from stealing from a box with no lock. They can protect a Post Office Box in the post office as that will have a lock and key.
Of course you should consult your divorce attorney.