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So I just finished with chat - they had me reset the SMC and a pram reset. It still was not working, so while she was off trying to figure the problems, I was playing with my cords. Hopefully I did not have 1 end from 2 different HDMI cords plugged in. Or the reset fixed the problems, plus unplugging the cords. I did also verify that I could have a 4k monitor and 1080p plugged in to my Mac mini....
 
Unfortunately, it's a little more complicated than that.

The UHD 630 in the 2018 Mini should be able to do 1080p @ 120Hz, but I've not personally verified yet that it does in OSX.

According to the specs for his monitor, its DisplayPort can accept up to 165Hz, but the HDMI port is limited to 60Hz. So in theory the HDMI port should just work. My suspicion though is that when the monitor's capabilities are being enumerated by the UHD 630 driver in OSX, the driver is getting confused and erroring out.

Thus it might be worth submitting a bug report to Asus/Apple in the hopes this will get fixed someday.

I am curious to see if OP has any success with using a USB-C to DP cable to connect his monitor.
The Intel specs are fairly useless once stuck inside a Mac, Apple will limit things in hardware and software drivers.
 
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