I don’t know if this solves the pink screen problem, whatever it is. I’m not a techie so this is all I can offer.
I got my Mini end of December and the pink screen problem just started now. I had no pink screen until I went to change the Sleep / Wake settings. Then I started getting the pink screen with desktop barely showing through. So think when / if you changed your settings from the default. Maybe your problem started after that.
Returning settings to default doesn't fix it. I also tried to check / uncheck different sleep / wake settings, but didn't work either.
I have the latest Mac Mini 3 GHz
Intel Core i7, 16 GB RAM Yosemite 10.10.2.
External ASUS PA248 monitor via HDMI.
I know everyone has different set-ups with slight variations in the problem, but maybe this will help some people. It seem to have worked to solve the pink from appearing, but I don’t think it has solved he actual problem. At least if I have to go to my computer every half hour, I don’t have to wear out my monitor button by having to turn it on all the time just to get rid of the pink screen.
I know people want their Mini to sleep but for these instructions your Mini will have to remain awake all the time.
This is my monitor set up.
Screen saver set to go on in 10 minutes.
Monitor shuts off in 15 minutes.
The Mini stays on all the time, no sleep or wake cycles.
1. Go to ENERGY SAVINGS
2. The only thing I have checked is, “Prevent the computer from sleeping automatically when the display is off. Leave the rest unchecked".
3. Then go to SCHEDULE Uncheck these,
START UP OR WAKE and SLEEP settings.
Hit OK
Exit ENERGY SAVINGS.
Let your monitor turn off, come back later. Sit down and re-try to to turn on your desktop. DON'T click away on your mouse or move it back and forth furiously like you want your desktop to load RIGHT NOW. Well I did that and the system didn't like that and the pink was back. It seems the system needs a few seconds to load up the desktop. Click the mouse button once, or move the mouse a a TINY bit. Wait a bit and the desktop should appear WITH NO PINK SCREEN, hopefully.
Hope this helps.