I'm fairly sure it's connected via the outlet just to the right of it... if I disconnect both outlets, should I be able to pull the wire out of the old outlet? Would it be attached any places inside the wall?
Cheers
First rule, make sure the breaker is off and there is no power to either oulet.
I'm not sure why you want to unhook both outlets. From the oulet on the right, just remove the wire going to the oulet on the left. Tape up each wire in the cable seperately, so they are not shorted together, (just in case power comes from somewhere you didn't expect) Then remove the oulet on the left from the wall. If the wire is stapled within the wall, just disconnect the wires from the oulet. I'd tape the wires seperately again and push it out of the way. When you turn power back on, the outlet on the right should still work.
Cut hole for doggie door, when you have that big hole, you might be able to remove
the staple and wire if needed.