I cannot find any property for a block in code which corresponds to Expire Date property in CMS. As far as I can see, Episerver.Core.PageData has a property StopPublish, which, as far as I know, corresponds to expiration date in CMS. But Episerver.Core.BlockData has no such property.
Is it not possible to set the expiration date for a block?
You'll have to cast it to IVersionable first - (currentBlock as IVersionable).StopPublish