On a standard J box, you can have the wire (Romex) enter from the top, bottom or the back. The only crucial thing is to make sure that Ground (usually bare copper or in green colored insulation) goes to the ground on the receptacle (usually a green screw near the bottom of the outlet and connecting to the "frame" of the outlet); Black (hot) goes to black, which is usually a gold colored screw on the right side of the outlet as you are looking at the front ; and White (neutral) goes to white, which is usually a silver colored screw and is on the left side of the outlet as you are looking at it from the front.
If you have enough wire so that if you were to cut it at the box and you could wire up to a new outlet without any strain on the wires, I would do so: cut at the old box and discard.