Hi Tammy:
Many of the older stoves used a similar door hinge system.
When the door is fully opened it can be removed in the following way.
It's much easier with two people.
With one person on each side, lift near the hinge (closest to the stove) then pull away from the stove and at the same time, lift the handle end of the door.
There is a tab and a notch on the hinge arm that has to slide past the retainer.
To re-install, the hinge has to be set for the "door open position".
Slide the hinge arms into the slot so that the tab and slot engage in the correct positions.
Hope this helps.
Cheerfuls. .