I just removed part of our cabinet during demo and our kitchen has a hardwired garbage disposal to a junction box on the wall. 
I want to disconnect my disposal during demo and save it for reuse in our remodel.
How do I disconnect the disposal from the junction box and reconnect the loose wires in junction box so that the path of electricity is still maintained for the other parts of the kitchen?
I'm pretty sure I know how to disconnect it…
(1) Turn off power at the breaker box
(2) Open junction box and disconnect wires that goes to the disposal
(3) …what do I do next with the loose wires? (I guess I should open the box and take a picture)
Best Answer
It seems like you know most steps leading up to it. Based on that it seems you only want to know what to do with the wires once disposal wiring is removed.
I would simply take wiring caps and place one on each exposed wire and then wrap each wire with some electrical tape further ensuring the caps stay on and do not become exposed if touched or caught when working around the wires. If you are keeping the junction box I would still use the same method but place wires back in the box and and screw the plate back on. Pull wire to sit inside of junction box or just place the end in the box and screw plate back on.