The only way is via some network solution such as Luna Display, Apple Screen Sharing, or some other VPN apps.
However, with Photoshop and Lightroom as your apps, these are definitely not a solution for a whole variety of reasons the prime of which for these is the reduced bit depth and color palette that these solutions deliver to the display.
You need a dedicated monitor for the new Mini which will not only give you proper color and luminance (once calibrated) but will draw a lot less watts than an iMac which would be running at full power with the above solutions.