How do I clean out my system data when storage is full?

The final word from Apple on Managing the " Other/ System Data “ Category

Other / System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

There is Purgeable Space and there is Empty Space.

Purgeable Space which is Controlled by the Operating System. When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur  

The links below will assist in identifying what is taking up space on the Internal Drive and provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

➡️ How to delete Time Machine snapshots on your Mac.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shot on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then will the Snaps Shots be transferred to the External Drive and deleted the Internal Drive. ⬅️

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

Notation - If the user is using a cloning software like Carbon Copy Cloner - and https://bombich.com/kb/ccc6/automated-maintenance-ccc-safetynet-folder suggest tweaking the Safety Net Feature in this software. It may be making additional Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

Does this computer have many Adobe Applications installed ?

You may check with Adobe of how and where to find and remove their cache files which and grow to xx GBs of used space on the drive

Understand, cache files of any type will be recreated as the Operating System or Application deems it necessary

The System Data is what was called Other Category earlier. The Other category is a potpourri of files which can include:

• System temporary files

• macOS system folders

• Archives and disk images (.zip, .iso, etc. - often found in the Downloads folder)

• Personal user data

• Files from the user’s library (Application Support, iCloud files, screensavers, etc.)

• Cache files: browser, Mail

• Mail messages & attachments

• Fonts, plugins, extensions

• Safari reading list

• iTunes backups

• Crud resulting from jailbreaking your iDevice

• Game data

• Saved data files

• Call history

• Notes

• Media

• Voice memos

• Other files that are not recognized by a Spotlight search

• Media files that cannot be classified by Spotlight as a media file because they are located inside of a package

• Files created and modified by other user accounts on your Mac.

They can be located anywhere on your hard drive.

The files that you have control over are located in the Documents, Downloads, Pictures, Music Movies and (to some extent) the Application folders.  You can use this free app, GrandPerspective, to find the largest files on your drive so you can determine if they can be deleted or moved to an external HD for storage.

Note: you can empty the Downloads folder after the apps and/or updates that were downloaded have been installed or applied.  Some users have found a couple of Gigabytes of files in their Downloads folder which are no longer needed. 

That’s not a bucket of stuff, it’s the size of various files and caches that don’t fit in the other categories shown.

How to reduce that usage? Delete some of what you are using the Mac for.

Frustated with "others" storage in mac. - Apple Community

You’re not going to link the more succinct answer: this Mac is just too small for your needs.

Given you’re on a Mac mini, an available option short of replacement is to migrate to an external USB 3.x, USB4, or Thunderbolt SSD. (Here is the general setup; this is for iMac, but mini is ~the same.)