@Jinbeifan1: demons? No. In the same fight, she took over the demon's abilities. And, what she's saying, she controls them.
Devil Fruit users are already no longer human. As long as any other explanation does not surface, we can only go by "Devil fruit users", thus powers of devils that inhibit their bodies. Mirajane can either absorb these abilities or control the users themselves.
"gain control over you" is most likely referring to what I just said. Her opponent was also using a control based curse called Macro, which pretty much cancelled Mirajane's own Takeover magic which is also a control based magic, both of their respective abilities from working on each other. That however is not a limitation with any devil fruit user that I know. Not saying the likes of Doflamingo, Kizaru, Akaino or Aokiji or even Luffy himself cannot land a hit on her.
Just saying, she has a demon called Sitri, one thats even stronger than Halphas and naturally faster at that. Mirajane only need to think here in order to takeover Luffy's devil fruit abilities.
That's because she was a demon! She couldn't control her so she had to absorb part of her power instead! Mirajane does NOT have the ability to absorb multiple types of magic, or she could become a dragon slayer, a make or a requip mage. Take over mages can absorb certain species to add to their power. Lisanna is animals, Elfman is monsters and as Mira said in the post, she absorbs demons. Show me a scan of her copying anyone else's ability that's not a demon, until then you're sorely mistaken about her power, or else her and her family would be the strongest mages in ft