Reddit mentions of Cable Matters Mini DisplayPort to DVI Cable (Mini DP to DVI Cable) in Black 6 Feet - Thunderbolt and Thunderbolt 2 Port Compatible

The following is an excerpt from Stack exchange. I cannot confirm if this works, but it might be worth looking into for you.

User - Tohster
Apple's specs show that the late-2014 (which is still being sold today, October 2015) Mac Mini can support up to two displays using its HDMI and thunderbolt ports.
I've confirmed this by trying to plug in 3 monitors directly into the ports on the Mac Mini (two via thunderbolt, 1 via HDMI), with the same results as the OP...one of the monitors is not driven.

The following 3-monitor setup worked for me:

• Late 2014 Mac Mini with 8GB RAM (purchased Oct 2015)
  
• 3 monitors, each with 1920x1200 resolution
  
• Monitor 1: driven by Mac mini HDMI port (HDMI-to-HDMI cable)
  
• Monitor 2: driven by Mac Mini thunderbolt port (I used this thunderbolt-to-DVI cable)
  
• Monitor 3: driven via USB 3.0 adapter (I used this one from CableMatters and have had zero issues with flicker/performance, although I am not trying to play games or watch video on it...I use it for work).
  
  Some notes:
  
  
• You can use a different USB adapter (there are several on the market) but make sure that it's Mac compatible. I previously tried one that had "beta" Mac support and it was terrible.
  
• Thunderbolt-to-HDMI and Thunderbolt-to-DVI cables are really mini-displayport to DVI/HDMI cables....the Thunderbolt ports accept mini-displayport connectors.
  
• For the two natively driven monitors (#1 and #2 above) you can use any combination of HDMI<->HDMI/DVI or thunderbolt<->HDMI/DVI cables depending on what your monitor accepts.
  
  Source:
  
  https://apple.stackexchange.com/questions/159382/hook-up-3-monitors-to-mac-mini-late-2014

Just that there's no point buying anything expensive. "AmazonBasics" is great because they don't overcharge.

mDP to HDMI: https://www.amazon.com/AmazonBasics-Mini-DisplayPort-HDMI-Cable/dp/B0134V3KIA/ref=sr_1_1?ie=UTF8&qid=1511801974&sr=8-1&keywords=mini+displayport+to+hdmi+cable

mDP to DVI: https://www.amazon.com/Cable-Matters-DisplayPort-ThunderboltTM-Compatible/dp/B00DJCB83O/ref=sr_1_1?ie=UTF8&qid=1511802068&sr=8-1&keywords=mini+displayport+to+dvi+cable

You just need $20 in adapters. This one and this one.

I run three monitors, all different resolutions, for multitasking. I have my main, center monitor connected to my GTX 970 via DVI. My 970 has one DVI, one mini HDMI, and 3 mini DP outputs.
To run the other two monitors, I'm using my processors (i5 3550) integrated graphics. One monitor is connected via DVI, and the other by VGA/D-Sub.

I want to connect all three of my monitors to my 970, so I don't have to use the iGPU at all and avoid some driver and compatibility headaches. Preferably, I would just want to use an adapter to have the mini DP ports on my 970 go to the DVI in ports on my other two monitors. None of these monitors support HDMI or DP of any variant.

Would using an INACTIVE converter such as this work for what I want to do?

That's pretty good actually given it already has the quad core i7 chip if you factor in the cost to upgrade to one plus it comes with a charger and the FHD TN panel. To clarify though it doesn't have a Thunderbolt port as mentioned in the 'about/info' section, what that is is a miniature DisplayPort or mini-DP which look similar. But yea that's a pretty good price and the seller looks safe.

Edit/Add* For systems with mini-DP you'll wanna grab one of these cables here which work wonders (I use one with my T430):

https://www.amazon.com/Cable-Matters-DisplayPort-ThunderboltTM-Compatible/dp/B00DJCB83O/ref=pd_lpo_vtph_147_bs_tr_t_1?_encoding=UTF8&psc=1&refRID=VWGVFFE80EP69A2CT3HR

Isn't DVI-D better than VGA in most cases though?

Feel free to correct me if I'm wrong, but from a cursory Google search that's what I've seen.

Would a Thunderbolt to DVI adapter like this one work?