Just because she chopped off their arms and de-toothed them, wouldn't they still be clamoring to eat her, like all the other walkers?
As in the comics, removing the arms and lower jaws effectively removes the ability to eat which seems to somehow tame the walkers.
In episode 3x03 (Walk with Me) Milton speculates on why Michonne may have taken off the zombies arms and jaws. He theorizes that taking their arms so that they can't grab anyone resulted in them becoming more docile. He also proposes that because of that they lose interest in feeding.
"Take away their ability to eat, they lose interest in doing so."
Frankly, I don't see how this would work and I strongly believe it's only in there because it's in the comics and because it's different. From what we've seen so far Walkers always yearn for your flesh, even if they're almost dead. Even if they're unable to move. They seem to react to certain stimuli but they don't behave logically. As such, I'd expect these pet zombies to still try and eat Michonne and generally get in her way by invading her personal space.
My guess would be the zombies operate on an instinctual level, and on some level the tamed ones know they can't eat, so they don't try.
Possibly having to do with muscle feedback: the zombie brain realizes its jaws and arms aren't working so it stops trying to use them to conserve energy .
Any answer is pretty much speculative, and the in-universe answer is most likely always going to be "it works like that because that's the way it works."