I would like to suggest that you should have more empty space on your HDD as having been suggested previously.
To this end, copy non-commonly used data (movies, music, pictures, etc) on your internal HDD onto another disk and then remove the copied data from your internal HDD. You can also remove applications that you do not use. Repeat this procedure till the USED space on your HDD is less than 200 GB.
You can then perform a check and repair procedure for your HDD.
A much better way is to reinstall OSX. Backup all your data and then reinstall OSX. After the reinstallation of the OSX, reinstall your applications and only copy essential data onto your internal HDD.
If you have a lot of data, you then either leave your data on an external HDD or replace the internal HDD with another one that has a larger capacity or install a second large HDD.
If you want to have a second internal disk, you may consider an SDD. For the Mac mini to better serve you, always get a disk of a large capacity (HDD: 1- 2TB; SSD: 256 GB - 1 TB) you can afford. If you do install an SSD, make sure that it is used as a start-up disk.