I use my 2011 Mac Mini as a media server and household backup system and have swapped out drives several times. (note: I have not actually used this cable, just found it and many others in quick search) But if you do want to go external, you could replace the video cable with a HDMI to VGA cable which would free up the Thunderbolt port. I too would recommend an internal SSD for the Mac Mini. Frankly, those high-end drives are probably not worth it in the 2011 Mini.
#Mac mini 2011 ifixit pro
If you want to spend more and get diminishing peformance improvements, you can get the 850 Pro or some of the other high-end drives. The Samsung 850 Evo drives are the most popular SSD's and they generally have a good reputation. Even though it'll be significantly slower than the 2015 MBP SSD, it's still the most cost-effective way to increase performance of the 2011 Mini after putting in 16GB of RAM. There is no way you can get that kind of speed on the 2011 Mini - the Thunderbolt is TB1 (10Gb/sec.) even if it was available to be used. The 2015 MBP has a 4-lane PCI interface, which is 2+ times faster. The Mini 2011 has SATA3, which, with the better drives gets around 500MB/sec. and then you probably won't use them again. For your situation, I think that may not be a bad choice considering that if you do it yourself, you'd have to spend some money for the tools, etc. There was a poster a few months back who had it done at an authorized Apple repair shop here in the US and they charged $60 for labor which I don't think is a bad price. People have broken stuff while doing this. Opinions vary as to whether it's easy or difficult.
![mac mini 2011 ifixit mac mini 2011 ifixit](https://d2rormqr1qwzpz.cloudfront.net/photos/2012/03/16/55-26882-ifixit_macmini_teaser.png)
I've done the remove-the-logic-board method for both of my Mini's. (The 2012 is more similar to the 2011 than is the 2014.) There is an "easy" method if you just work with the "Lower" drive bay - the bay that is accessible when you open the Mini.