Mac storage basics · iPhone and iPad backups and updates
Can I keep iPhone backups on an external drive instead of my Mac?
Short answer: Finder can't change the backup location, but the backup folder can be moved to an external drive with a link left in its place; Storage Studio does this from What's Using Space. The drive must be connected when you back up.
Finder has no setting to choose a different backup location; it always uses the folder in your Library. The common workaround is to move that backup folder to an external drive and leave a link in its place, so Finder writes through to the drive — but then the drive must be connected whenever you back up.
Storage Studio does this for you. In What's Using Space, your iPhone and iPad backups appear under Space held by backups, and Move to fast drive… copies them to the drive, checks every file arrived, and only then frees the space on your Mac. Move back… returns them any time. Alternatively, back up the device to iCloud and keep only an occasional local backup. See moving iPhone backups.