This Apple Community thread indicates that your Mini can drive a 3840 x 2160 monitor over mDP – but not at 60 Hz. Note that the link to the old (and relevant) Apple Support article "Using 4K displays and Ultra HD TVs with Mac computers" now goes to some other article.
Can the Mac Mini late 2014 monitor 4k dis… - Apple Community
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Going just by Apple's technical specifications, it's not clear if the Thunderbolt 2 (Mini DisplayPort) ports on that Late 2014 Mac Mini support any resolution higher than 2560 x 1600 pixels at all.
Mac mini (Late 2014) - Technical Specifications
"Support for up to two displays at 2560 by 1600 pixels, both at millions of colors
Thunderbolt digital video output
- Native Mini DisplayPort output
- DVI output using Mini DisplayPort to DVI Adapter (sold separately)
- VGA output using Mini DisplayPort to VGA Adapter (sold separately)
- Dual-link DVI output using Mini DisplayPort to Dual-Link DVI Adapter (sold separately)
HDMI video output
- Support for 1080p resolution at up to 60Hz
- Support for 3840-by-2160 resolution at 30Hz
- Support for 4096-by-2160 resolution at 24Hz"
