I checked my interactions with Apple and Wolfram re Mojave. I was a beta tester for Mojave on my 'spare' computer (a 13 inch MacBook Pro). I tested each beta with Mathematica 11.3 -- actually Wolfram Desktop from a Wolfram|One trial, since I don't have a third license. I had no issues with the program itself, although there were issues with the download manager.
When I installed macOS Mojave on my two main computers (a 2017 27 inch iMac and a 2016 15 inch MacBook Pro), there were issues with the installation. I ran disk utility immediately after the installation, and it found orphaned dream object. Apple support said that these were left-overs from the installation, and they should go away. I know how entropy works, though.
I ended up using recovery mode (cmd-R on restart) to erase the hard drive, re-install Mojave, and then restore from a back-up. On my MacBook Pro, I saved the contents of my documents folder and did a clean install.
After I did that, there were no more problems with Disk Utility. In addition, inside the ~/Library folder, there was a lot less stuff from Wolfram. The download managers, and some other installers apparently do not clean up after themselves very well.
These computers had been updated from older installations over the years, and so there was a lot of cruft in the System Folder (and elsewhere). Depending on your history, the same may be true for you. It is possible that your issues have to do with obsolete stuff in the $UserBaseDirectory.
If you have no issues with other apps, or with Disk Utility, you may simply want to remove the Mathematica folder from within ~/Library (aka $UserBaseDirectory). When you restart Mathematica, you will need to re-authorize. I would keep the old folder somewhere, especially if you have custom stylesheets, palettes, or other add-ons.
Since it is only an issue of download time (unless you saved the installer), if you have invested this much time, it makes sense to install a fresh copy of Mathematica. Note that doing this without setting the $UserBaseDirectory to its 'new state' is a waste of time in most cases.
NOTE that on macOS, the $BaseDirectory should not exist. It was deleted a couple of macOS upgrades ago for security reasons, although the Wolfram documentation and FAQ still refer to it. It is inside the system's Library folder, as opposed to the User's Library folder. If you have a Mathematica folder there, you should probably remove it. Mine disappeared with the OS update automatically. Wolfram Support will tell you that you can manually copy the Mathematica folder from your User library there, but in my opinion, that is asking for trouble.
In the 'dark ages', when the OS came on DVD-ROM, I would always do an erase and install whenever there was a new OS. It is a lot more convenient to simply upgrade in place, but there is a price. I found stuff from more than 10 years ago inside my system folder that really should not have been there. My MacBook Pro seems zippier, but that could just be an impression. I really had few, if any problems before, but I did recover significant disk space. I also managed to lose preferences, etc. for software that I no longer use.