Kind of a hacky option and would need to be tested, but you could schedule a shutdown (this could be done several ways) and kill the power to it once it’s shut down (using some kind of smart plug). Enable start up automatically after power failure (in the energy saver settings), and trigger the power to turn on to the Mac when you return so it boots back up.
I’m not sure if the automatic startup on powrfailure requires an expected reboot, or if it will always start up when it starts receiving power. So that would need to be tested, and could be tested by simply unplugging it and plugging it back in after change the energy saver setting.
If it’s just for power savings though, I’d question how much energy the mini actually uses while sleeping and if it’s worth it to shutdown vs just sleeping.