You need to use a PC or program capable of reading a Linux partition.
If you are on a windows PC try Diskinternals Linux Reader (free).
Or use a Linux live CD/DVD.
When you have done that and got everything up and running again, the first thing you should do is set up one of these that will create and copy your snapshots off the card automatically:
To a NAS: Samba Backup: Create and store snapshots on a Samba share
To Goggle Drive: Hass.io Add-on: Hass.io Google Drive Backup
To DropBox: Hass.io Add-on: Upload hassio snapshots to Dropbox
To NextCloud: [New Addon] Snap-Shipper - Webdav backups (and probably other ways to later on)