1. Try resetting the NVRAM & PRAM as per > About NVRAM and PRAM
2. Make sure that your both your Mac Mini's Software and Firmware are up to date.
If it is a new Mac Mini, then you may need to wait a bit for a Firmware Update to correct the problem.
Alternatlly if a different DVI cable does not solve the problem, then you might want to try a MiniDisplay Port to VGA adapter and a VGA cable connected up to the Thunderbolt/MiniDisplay Port to see if you can get full 1980x1080.