Excessive System Data storage (310gb)

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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

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

Is there a Suite of Adobe Application  used on this computer ?

They may create some very large cache files that can be removed. Though, the Adobe cache files will be recreated as the Applications needs them.

https://helpx.adobe.com/ca/premiere-pro/kb/clear-cache.html

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.

System Data used to be called "Other Category" in previous systems. 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 and Movies 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. 

It is likely your data being mischaracterized by Spotlight.

System Data was once called "Other" as it didn't match any of the categories that were reported (Documents, Movies, Music, etc).

That storage display is created dynamically by Spotlight. If it can't figure out what category you place the item, it uses System Data. There is some real "system" data in that category, but it also can be a lot of your data it can't figure out. Some things that can cause large System Data are runaway logs and Time Machine Snapshots. Those are about the only things you may be able to remove.

Use a program such as GrandPerspective or OmniDiskSweeper to figure out exactly what is taking up space and deal with it individually. There is no way to manage it in macOS.