Disclaimer: My $dayjob is with a government contractor, but I am speaking as private citizen.
Talk to your organization's computer security people. They will have a standard procedure for getting rid of dead disks. We on the internet can't know what they are. I'm betting it involves some degree of paperwork.
Around here, I give the disks to my local computer support who in turn give them the institutional disk destruction team. I also zero-fill the disk if possible, but that's not an official requirement. The disk remains sensitive until the process is complete.
Jim