Reset Mac mini to as new configuration

You'll need to boot into the Recovery volume (boot with the Command + R keys held down  - Intel Macs) or  (How to Boot an M1 Mac into Recovery Mode), erase the drive as show in the screenshot below and reinstall the system. Then when it starts booting the first time use Migration Assistant to transfer your user data from your Time Machine backup or some other backup of your data files.

If you can't erase #1 the first time start with #2 & #3 and then do #1.

And then there is the

Scorched Earth Method 

This method will WIPE ALL Data and there is No Recovery - Period.

>> Only works on Intel Based Apple Computer <<

To perform this action will require booting from a Bootable Installer. 

The Bootable Installer can Only be performed on an Apple Computer 

This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer. Example : Bootable Installer of Big Sur would have to be done on a computer that Qualifies to run Big Sur.

Notation: If the computer being used to perform this action is Too New or Too Old to qualify to run the version of macOS - this computer can not be used.

Alternative is, to gain access to a Qualifying Apple Computer from a family member, friend or associate.

1 - Shutdown computer and disconnect all external drive Except the newly created Bootable Installer.

2- Restart and immediately hold the OPTION key until the Startup Manager appears and choose the USB Drive. 

3 - It will present options >> Disk Utilities >> View >> View ALL attached Drives. 

4 - Choose the Upper Most Drive ( not the volumes indented and list below ).

5 - The drive normally is called Apple Media or Apple SSD - that is the drive to Erase and format as APFS with the GUID Partition Map. This applies to macOS 10.14 Mojave and above. 

6 - Once that is done >> backup out of Disk Utilities and choose install macOS. 

7 - Follow the prompts and it may automatically reboot several time. 

8 - Upon a final reboot - Setup Assist will present with the newer version of macOS.

Not sure what you're referring to but just tested that method and it got where I wanted to go except I was a version behind where I was originally.

So you're right, using a bootable USB thumbnail installer for the version you want is the most expedient way to go. However, I did the data transfer from a clone on an external SSD and it went much faster than from my much slower Time Machine HD. That's why I always have a clone on an external SSD as well as Time Machine backups.

Old Toad wrote:

Not sure what you're referring to but just tested that method and it got where I wanted to go except I was a version behind where I was originally.

So you're right, using a bootable USB thumbnail installer for the version you want is the most expedient way to go. However, I did the data transfer from a clone on an external SSD and it went much faster than from my much slower Time Machine HD. That's why I always have a clone on an external SSD as well as Time Machine backups.

Referring the Scorch Earth as in Wild Fires in your neck of the woods or pond for Old Toads lol

Above method may work for the OP as " Is it possible to completely wipe my hard drive "

Fortunately for us most of the fires are in the northern part of the state. At least at the present time. We're down close to San Diego (about 50 mi north). But it's not been a good year fire-wise anywhere in the world.

I spent some time in England in the 80's (Greenham Common) working for a couple of months and did not have the kine of weather that's being experience there today. That's worse that what the US is experiencing as we're more inlined to have A/C installed in our homes and buildings.

Scorched Earth - Not affect in you area ?