I'm not sure Disk Utility still allows the secure erase option of writing zeroes to the whole drive even when using a hard drive. It is possible it will pretend to go through the motions, but not do anything (I've read this happening in several posts on these forums). You definitely should not do this when using an SSD as it causes excessive wear on the SSD and it won't do what you think it will due to how SSDs work internally.
If you want to make sure your data is inaccessible, then enable Filevault on the drive. Once Filevault has finished encrypting the drive you can perform a normal erase with Disk Utility which will overwrite the Filevault encryption key protecting the previously Filevaulted data.
There is an option to use the drive's built-in hardware secure erase feature to zero out the drive. Traditional hard drives and many SSDs include this hardware feature, but it requires a Linux utility to access the hardware feature. If you want to try this option, then create a bootable Parted Magic USB drive using Etcher (Mac/Windows/Linux). Parted Magic is customized Linux utility boot disk.
Option Boot the Parted Magic USB drive and select the orange icon labeled "EFI". Once it boots to the desktop you should see an icon on the desktop for erasing drives. To utilize the drive's built-in hardware secure erase feature you need to select the "ATA Secure Option" (this is the only safe option for SSDs) which will prompt you to sleep & wake the computer. It will also ask you for a temporary password so keep it simple with something easy to remember like "abc". If the secure erase fails or is interrupted, then you will need this password to unlock the drive later on. For an SSD the erase will usually only a take a minute or two. For a hard drive it can take several hours.
The last free version of Parted Magic is available from the MajorGeeks' download link here. I know this disk works with 2012 or earlier Macs. I've never tried it on a 2014 Mini. Here is an article detailing the procedure using the latest version of Parted Magic which has a slightly different version of the app, however, the basics are similar.
https://partedmagic.com/secure-erase/