Will a Mac Mini work well for Graphic Design?

not huge difference unless you do heavy video work and need a 4GB card which only comes on the high end, but upgrade the i5 on either model and you might get a few more viable years out of that box as a production system along with the i7 and 16GB RAM (or more) would benefit as well. The midline system would be a beast with this config, appears you cant upgrade the GPU on the middle one but if you are not doing HD video editing 2GB is very good and you could always get something much more powerful down the line with TB2 to GPU externals that are out there.

Apple will charge you $200 for the RAM but you could do it cheaper aftermarket or for ~$259 you could get 32GB RAM, you have a workstation at that point and the LCD is really amazing.

Macsales, Corsair, Crucial all make Mac Compatible RAM

https://eshop.macsales.com/shop/memory/iMac/2012_27/DDR3L

Depends on how great your DTP needs are.
If you are working on web assets you can likely get by

if you are working on hi-res or print assets with multiple layers that system will show it's limits quickly.

If you plan to work with CS Adobe claims it's not compatible with OS 10.12.5 which is current so your workflow may or may not work flawlessly. Photoshop seems to be the most stable but AI and ID can be tricky.

Will a Mac Mini work well for Graphic Design?

It might, but pairing Apple's least powerful Mac with high end graphics software wouldn't be the best option.

Also, do the Minis allow you to add a SSD?

The best option would be to order it with the optional Apple SSD installed.

Also, I'm not a fan of having the HD and monitor as one unit... if one dies you have to replace the whole thing.

Not true, iMac HDs are replaceable.

You would need to purchase RAM at the point of purchase (Max is 16 GBs), it's not upgradable at a later date.

The biggest drawback with the MacMini would be the limitation of the Intel HD Graphics 5000 or the Intel Iris 5100 graphics.

Couldn't I just add more RAM to the Mini?

No, the new MacMini's RAM is soldered to the logicboard.

MacMini's don't have graphics cards, you have a choice of 2 different Intel graphics chips, also soldered to the logicboard.

Just look at the specifications for the iMacs, the higher end models have significantly improved graphics capabilities compared to the Mac Mini.

Top end MacMini: Intel Iris graphics

Top end iMac: AMD Radeon R9 M395X with 4GB video memory, not to mention a 5k display.

the Pro would not be the way to go right now, it's over three years old with no improvements at this time.

the iMac is what I've been deploying for high end production and I've deployed over a dozen of them so far.

the 27" model has a phenomenal display and can be upgraded to 32GB RAM later

the 20" model also has a great display, can be upgraded to 16GB RAM but only at time of purchase, not later.

Either model can be configured with an SSD.

The 27" has an option for a 4GB GPU, the 20" does not. The 20" will come with an intergraded card or GPU, but the base model should be avoided, it's not a good production system, it's closer to an iMac for people who don't want an iPad.

keep in mind some of the GPU graphics technology for design will not combine VRAM on two cards so 2 cards with 6GB RAM might only give you a total of 6 GB RAM (not the 12 you actually have between the two card) but it might combine the processing power so dual cards. This is all dependent on what technology you plan to use. Check the app to see what it supports.

Case in point Nvidia CUDA is popular for many CAD/CAM apps but it wont run on an AMD GPU and default to CPU which is absurdly slower in come cases.

If you are a hobbyist and time doesn't matter, the Mac Mini would work.

If you are actually doing work on the Mac to make an income from it, I would say you will not be happy with that decision in the long run.

Yes I recommend them. I have about 12 graphics techs on them, one of them is using it for video editing and 3D post work.

On the Creative Cloud DTP the machines with the 2 and 4GB VRAM does not make much of a difference but it does for the heavier prodution system, it's a mix of Nvidia and ATI, you can't get a newer on with an Nvidia card now and while I prefer the Nvidia's the ATI's are very capable.

We are running quad core i7's and 16GB RAM. The systems are very responsive, I have AppleCare on all of them but only had to use it once for an Nvidia GPU issue that was covered otherwise it would have been an expensive fix. I don't have anyone doing any web dev on them other than some website production but the vast majority of it is print and touchup with high res. I replaced dual Xeon 2009-2010 mac pros with the i7's, overall the iMacs have been faster even against the dual xeon pros but they were the older pros. Apple may update Pro's this year or next but they have not said when we might expect that so it's all conjecture.