Shutdown the Mac Mini.
(if you can not shutdown not from the screen hold the power button for 10 seconds)
Reset the SMC, as per > How to reset the System Management Controller (SMC) on your Mac - Apple Support
(check the display connections to insure that they a firmly connected while the power cord is disconnected)
Then restart the Mac Mini with an NVRAM reset, as per > How to reset NVRAM on your Mac - Apple Support
(trun on the Mac Mini and hold the Option Command P R keys until it chimes 3 times, then release the keys)
If that does not fix the pink screen problem, then you will need test it with a different display, adapter and cable.