Good advice above. SSD is the key to improving your performance.
A few approaches:
1. Tear the Mini apart and replace the HDD with a 1 TB SSD (costly, doesn't solve the capacity issue you are nearing).
2. Same, but put a 128\256\512 GB SSD in and get a
data doubler kit to keep your 1TB HDD and
create a Fusion Drive of 1TB +128\256\512GB.
3.
SSHD. Seagate Firecuda for instance is a 2.5" 2TB hybrid drive, not as fast as SSD, but considerably faster than HDD.
4. External boot drive on USB3. Here too, SSD will be fastest, SSHD is also going to be better than current HDD. If RAID is desired, OWC has USB3 Drive Enclosures with slots for 2-4 HDD\SSD\SSHD drives that can mirror (RAID1), or RAID5 (3+ drives).
If replacing internal drive, choices are to clone the current drive to the new drive before replacing (use Carbon Copy Cloner or similar), or install fresh OS to the new drive(s) and restore from Time Machine (effective but slower). In both cases, prepare the new drive while externally connected (USB adapter comes with many kits), then do the physical replacement. If you go route 1 or 3, you can keep the 1TB drive in a USB adapter for additional external storage.
If you go the Fusion route, it will destroy all data on the existing disk, so make sure you have a good TM backup.
Same for external drive, clone to the new drive, or install fresh and restore TM to the new drive. In this case, after preparing the external SSD\SSHD, reformat the internal drive and use it for extra storage.