Do you delete data from media? Do you think there is no way to recover it?
Check if you are right.
If you delete data with the help of specialized software, you cannot be sure that no one will recover a part of it. In fact, the software overwrites a new payer of data, some of it propably can be recovered.
Do you erase data with a specialized, good quality degausser? It’s a good idea! If you use professional equipment, the data cannot be recovered in any way.
See professional degaussers here: degaussers for data erasure
If you physically damaged the medium, it will be difficult to recover the data stored on it. But … it is possible. That is why companies that care about the highest standards of data destruction first degauss the media and then physically shred it. If you only have a media shredder, try to damage the media as much as possible. Damage it in several places or crush it into very small pieces. This way you will minimize the risk of recovering some data (the more damaged / fragmented the data carrier, the more difficult it is to recover the information).
See professional destroyers/shredders here: data destruction with media destroyers