The trigger for a wanderer to respawn varies. Some respawn as soon as the player leaves the area, some respawn at certain times (e.g. daily), and some never respawn.
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You will need to respawn it. Get out of view to despawn. Save possibly then head towards it to spawn it in view. That should work as I've done this before for breeding purpose.
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Most likely, you have saved in front of the Mime Jr with it already loaded in, (i.e, when you open the game, it's in front of you). When you do this, you are simply resetting the same exact Pokemon over and over again. In order to get a Mime Jr with different stats, gender, nature, and shininess, you have to save in a spot where Mime Jr is despawned, (you can't see him), and then walk/bike into his area. This should produce the results you desire.
Hope this helps!