What exactly have you tried?
The easiest way to move your Photos to an external drive is to move the Photos Library to an external drive. This is described here: Move your Photos library to save space on your Mac - Apple Support
prepare the drive exactly as described above. The File System Format needs to be compatible with your system version (APFS or MacOS Extended (Journaled), the volume must not have been used for Time Machine backups and must not have any system software or backup software installed, it needs a wired connection and must not be a network share.
Then you can drag your Photos Library from your pictures folder to this external volume, test it thoroughly if it is working, and remove the library from the internal volume.
Are you using iCloud Photos as well on your iPhone or your Mac? To save storage with iCloud, enable the "Optimize iPhone Storage" in the Settings > Your Name > iCloud > Photos. But do not delete any photo you want to keep. When you are using iCloud Photos, deleted photos will be deleted everywhere, on your device, in iCloud, on any other device that is syncing with iCloud Photos.