Apple can get a bit fussy when people alter their systems either drives or memory (depending on the exact model and what you do). So you do need to use care here as you can damage things which Apple won't cover under warranty.
But before you decide on what to do, lets look at the options.
- Swap out the HD for a SSD
- Swap out the HD for a SSHD
- Add in a SSD blade drive
Unlike the older series this system only offers one SATA port and a custom connector for an Apple proprietary SSD drive. As you got the HD model you are limited on swapping out the HD with either the SSD or a hybrid SSHD drive as the easiest options without needing parts but more involved in taking apart.
The HD model does not come with the needed cable to add in a second drive here (blade SSD) but it can be added! Making a dual drive config.
As you are using Final Cut Pro you'll need to think through how big a project you'll be working on. A SSHD or a dual drive config maybe the better way Vs going with a SSD swap out. Many people find they tend to need more space than 500 GB. Remember, you'll need to keep about 1/4 of the drive free so you don't over wear the drive. Smaller SSD's need more 1/3 of the drive free.
What would I do here??
I would look at going with either swapping out the drive for a SSHD if the Final Cut Pro projects are small in size and a dual drive if they are larger.
Of the different options adding in the blade SSD is by far the least amount of work but sadly a bit more expensive. If you want to take the least risky path this is what I would do.
Review here the needed steps to swap out the drive: Mac Mini Late 2014 Hard Drive Replacement. You only need the replacement drive here. But if you don't have already a backup drive you'll need this as well: Startech 2.5" SATA to USB adapter so you can prep the new drive as well as migrate your stuff over to the new drive.
Here is what you'll need to add-in the PCIe SSD: Mac Mini Late 2014 PCIe SSD Cable Replacement. You will need the cable and SSD drive for parts. Unlike the swap out you can prep the drive once you have it installed and switch the boot up to the SSD or you can create a Fusion Drive.