In order to do a purge mid print purge (for a defined color change), you will need to operate the Mini through Pronterface instead of Cura.
Go ahead and load your model into Cura. Instead of opening the control panel, go to File > Save Gcode and pick a memorable location. Close out Cura, and open up Pronterface. Load the Gcode file directly into there and hit print. (Cura has a simple version of pronterface built in, and will look quite similar to what you’re used to.) It can be downloaded here if needed: https://www.lulzbot.com/support/downloads
You will notice Pronterface has a pause button at the top, which will turn into a resume button once paused. After pausing the print, you can move your printhead using the compass rose in the top left corner. Move it up, and away from your print to prevent drippage as you purge. As long as you make all movements through pronterface, it will automatically return to position once you hit resume.
If you do not disable motors once paused, it should be quite difficult to manually move the printhead which will keep everything squared. (So it won’t lose track of where it is in relation to the print.)
It may be an extra step with an extra program, but hopefully we will be able to get a Pause/Resume button added to Cura Pronterface UI soon!