Dual Monitor setup partially working with Mac Mini
Your Mac Mini has a NVIDIA GeForce 9400M graphics card which uses either 128 or 256 MB of DDR3 SDRAM shared with your computer's main RAM.

If you're wanting to simultaneously use the Mini-DVI port and the Mini DisplayPort, then your Mac Mini needs to be set up as follows:


Use the Mini-DVI port to connect a DVI or VGA display at 1920x1200 pixels 
Use the Mini DisplayPort (with an optional Mini DisplayPort to Dual-Link DVI adapter) to connect a dual-link DVI display at 2560x1600 pixels 


If you've got the right resolutions set and are using the correct cables, then you can try resetting the NVRAM to see if that resolves the issue.

Here’s how to reset the NVRAM on your computer: 


Shut down your machine. Yes, a full shut down, not just logging out. 
Press the power button and then press the 
commandoptionpr keys. You
have to make sure you press these keys before the gray screen appears or it won’t work. 
Hold those keys down until your Mac reboots again and you here the startup 
chime. 
Let go of the keys and let your Mac reboot normally. 


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).