Disk Utility not working.

Without knowing what "isn't working at all" means, I would suggest:

1. How to use safe mode on your Mac - Apple Support, which may restore functionality.
2. Since Disk Utility cannot be installed separately: Download/Install macOS Mojave 10.14.6 Combo Update

AlexPendragon wrote:

Is there a way to download a new copy of Disk Utility for Mojave? Mine isn't working at all.

There is no free standing Disk Utility.app however

You can re-install the combo update to sort one off anomalies like yours:

Combo update 10.14.6 https://support.apple.com/kb/DL2010?viewlocale=en_US&locale=en_US

It's a built in tool in Mojave, not something you can download. Try running it in safe mode, see if that works.