You haven't indicated which Mac mini you have.
If you are talking about a Mac mini released in 2018 or later which has USB-C (Thunderbolt) ports, those ports have native DisplayPort output. You would use a USB-C (male) to Mini DisplayPort (female) to hook up video. You would also want to hook up the USB connector on the display's "hydra" cable so you could control brightness and use the downstream USB 2.0 ports.
https://www.amazon.com/s?k=usb-c+to+mini+displayport+female+adapter
If you are talking about a Mac mini that has a Thunderbolt 1 or 2 port, those ports have Mini DisplayPort connectors and can double as Mini DisplayPorts.
If your Mac mini is so old that it only has a DVI port – no Mini DisplayPort or Thunderbolt port of any kind – then you probably are not going to be able to use that display with that Mac.