Don’t think you can do that OOTB automatically, but I’m sure you can do it using either a simple workflow (created with SPD or VS2005) or a event receiver… I’d probably elect to use an event receiver.

Yes, you can expire/delete the document automatically  using document  library event handler.

You could also employ the Records Management module in MOSS for document  retention, destruction and archival.

If you are using SPS2003 then you would have to use event handlers. If you are using MOSS2007 then yes you can do this my creating Information Policies and applying them to the document  library. In this case you would probably move your documents  from a Document Library to the new records center and use the built functionality for this. Obviously this could be achieved by also creating a workflow as Andrew stated earlier. I am a great believer in using the OOTGB functionality if it exists. In the case of MOSS2007 it does.

If you have MOSS installed you will have an expiration policy. If you
only have WSS v3, you'll need an event receiver. If you are running SPS
2003 or WSS v2 you'll need an event handler.

To set  start and expiration dates, the list or document  library has to
have a date  column exposed.