Removing dead assets from inventory and reports

I have a few assets that have recently given up the ghost, as the replacement items will have fresh asset numbers I'd like to mark the old assets as DEAD so that they don't appear in reports and we then know they're out of service or disposed of.
I've been filling in the EXPIRY DATE field but when I report on our assets it still includes the items with an expiry date. If they have an expiry date I don't want them to appear in out list of all assets as the chances are they've gone in the bin.
I know that I can report on assets WITH expiry dates, but that means then manually cross-referencing the two reports.

Is there any easier way to do this?