The "secure erase" option included with Disk Utility will only work for the old fashioned slow spinning hard drives since this writes zeroes or random data to the entire drive to overwrite every byte & sector. Apple does not allow this option for an SSD for several reasons.
- SSDs work differently than hard drives so it is impossible to write to all the blocks since some blocks are hidden from users.
- SSDs have a limited number of life time writes available, so this prevents users from accidentally wearing out their SSDs prematurely.
Generally just a simple erase will destroy all data on an SSD especially if TRIM support is enabled on that SSD, however, not all external SSDs support TRIM and you must use the following command in the Terminal app to enable TRIM support for third party SSDs (again....the external SSD must support TRIM....you can confirm that the SSD has TRIM enabled by checking the Apple System Profiler):
sudo trimforce enable
This will prompt you for your admin password. Nothing will appear on the screen as you type the password, so press the "Return" key to submit the password.
Many SSDs have their own built-in hardware secure feature, but this requires the SSD manufacturer's proprietary software. Check with SSD's documentation to see whether the external SSD supports TRIM and macOS.