If you are in doubt about physical health of your device (input-output errors, slow responding, extraneous sounds, there was a hit, fall etc.) it is highly recommended to address to specialists having specialized equipment. Any further work with the disk (including even starting up) may worsen the problem and cause complete inability to recover data. So any further attempts are at your own risk. Anyway it is possible only if the software can access the device (contents are readable), and device size is detected correctly (see the System Requirements).
Some errors may arise due to external reasons: bad contacts, power loss, etc. If a sector is not completely or incorrectly written then the device reports an error when reading such sector even there is no physical damage (a software bad). The device is working normally excepting errors when reading some sectors. In such case you should fix the problem source (check if PCB contacts are oxidised, replace wires, provide reliable power, etc.) and continue accessing the device safely if there are no new errors and no other problems (and of course there was no hit, the device is not responding slow, etc.) Anyway it is recommended to make a copy to a healthy disk.
During data recovery there may be multiple access to the same disk areas: programs usually scan the entire disk, then read again FS structures when building a directory tree for the selected volume, then read again FS and data when recovering selected files; different settings and software may be tried as well. The every additional attempt damages the device more and more.
So it is highly recommended to first clone the failing disk to a healthy device and work further with the copy.
In DMDE you may use the tool Copy Sectors to make the device clone. However the most safe and effective way is to use special equipment by data recovery specialists.
Normally OS may also work actively with the device damaging it more, interfere while working with it, as well may write unwantedly to the source disk. The recommendation on OS selection are in the section Installation and Run.
It is also recommended to use the mode IO SCSI (in Windows/Linux, or ATA Interface in DOS) as it is more fast and less aggressive.
To completely prevent the OS from working with the device partitions you may temporarily "switch off" a partition table. In DMDE you may use commands MBR Off / GPT Off in the Partitions window, then Apply, and restart the OS or reconnect the disk. Later you may similarly "turn on" the partition table (MBR On / GPT On).
Sometimes the device state does not allow entire cloning. Full copy may take an unreasonable time but you need to recover only some important files. In such case you may try data recovery without performing a full scan.
DMDE allows opening volumes and finding some files without preliminary full scan. You may try opening the volume if it is visible in the window Partitions just after selecting the device. You may also try opening volumes as soon as they appear in the results of Full Scan without waiting its completion. Make sure to Save scan results to avoid future rescanning in case of some failure. Open the volume and recover the most important files first and check if they can be opened/played.