It does exist. It’s called an EcoFlow or Jackery battery unit. It will be big and heavy, but that’s what’s needed to power a 120 volt mini.
The problem with using them is that it’s pretty inefficient to provide 120 volts for the mini’s power supply, only to down convert the voltages to what the logic board and components use. You’ll need way more mAh than you’d need to just power a MacBook.
On top of the inefficiencies going from DC to AC and back to DC, I imagine there would also be differences in the CPU throttling curves, the kind of fan used, etc.