Do you want the data to be deleted permanently from the index (disk) or just want it to be unsearchable while still retaining the data on the indexes (disks).
yes, as @PowerPacker pointed out below, you can run a scheduled search and set "run script" in alert actions to delete the index.
Take a look at the Delete command, here is the link.
You can make this as a scheduled search, make it run frequently to delete the data.
& another thing to remind of is, you need to have delete permissions enabled for you role to delete the data from index ( delete permissions are separate from admin permissions )