Mac Pro 2013 Freezes after 2 hours

Playing Safe- what does Safe mode do?

My Mac only runs properly in Safe mode

Use safe mode to isolate issues with your Mac - Apple Support

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    Be sure to backup your files before proceeding if possible.

1. Shutdown the computer, wait 30 seconds, restart the computer.
2. Disconnect all third-party peripherals.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences.
6. Start the computer in Safe Mode. Test in safe mode to see if the problem persists, then restart normally.
7. Use Apple Hardware Test to see if there is any hardware malfunction.
8. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
9. Repair permissions on the Home folder: Resolve issues caused by changing the permissions of items in your home folder.
10. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
11. Download and install the OS X El Capitan 10.11.6 Combo Update or 10.12.6 Combo Update or Download macOS High Sierra 10.13.6 Combo Update or Get MacOS Mojave now from the Mac App Store as needed.
12. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Reinstall OS X then click on the Continue button.

Playing Safe- what does Safe mode do?

My Mac only runs properly in Safe mode

Use safe mode to isolate issues with your Mac - Apple Support

The above may help you narrow down the problem. Determining what software is not loaded when using safe mode gives you a place to start. In addition to combing through the logs you may want to see if there are any panic logs associated with the freezes - Mac OS X- How to log a kernel panic. You should check that all the questionable software are upgraded to the most current versions - App Compatibility Table - RoaringApps. Same goes for macOS.

Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase icon in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Reinstall OS X and click on the Continue button.

I have good news, and I have Bad news.

The good news is that you found the problem.

The bad news is that you may be developing Bad Blocks on a rotating Disk Drive.

Data are recorded on your drive in semi-redundant form, and read back using error-correction Hardware. When block reads Bad (cannot be corrected) it may be read again in a series of steps up to 1,000 times before throwing error -36 I/O error.

On most drives, re-reading that one block 1,000 times can take as longs a quarter minute. That may be where the delay is coming from.

If its a Time machine backup, in regular cases you might be able to update that Time machine backup more easily than creating a new one. But you have waited so long that it may take all afternoon computing 'what needs to be backed up' before it starts copying files.

If you allow Time machine to run at least every-other day, it can use a system data structure called the File System Event Store to figure out what folders have changed, and the backup can start immediately.

Time machine is designed to run at low priority in the background. It works differently than most other backups.

A "complete backup" for a given date&time consists of all the unique files, plus links to all the older files in older backups that are already saved in that Backup set. It only adds the changed files to the large body of files it already has on the backup drive, and makes "hard links" to take advantage of the old ones already present on the backup set.

Since it is intended to work in the background at low priority, it computes 'what files need to be added to the backup set' FIRST. Then it makes certain there is enough space on the backup drive and consolidates older backups until there is space, and only THEN does it begin to add files to the backup set.

New backups rely on, but generally do not disturb, older backups, unless the drive is too full for the additions.

But as I mentioned above, the computation to determine 'what needs to be backed up' requires it to read the directory entries for every file, and may take all afternoon if you have not done a backup in the last few days. This could fail if the source drive directory is scrambled, but is unlikely to cause any disturbance or corruption in your old Time Machine backups.