Kamui vs Yata Mirror is interesting.
I don't think it could warp the mirror itself. There's nothing physically there for it to warp. As I explained in a post a while back
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, and as Kakashi has stated in the past
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, he can put however much chakra in to kamui that he desires. The bigger the object, the more chakra he puts in it. So we know that he has to base his kamui off the physical size of the object. I imagine weight, along with height and width effects his decision. That sounds logical enough.
So determining how much chakra he would have to use to warp the Yata Mirror would be where Kakashi's/Kamui's first issue would come in. As Owarij showed, it can change it's size to protect the user. Now the 2nd issue comes in the fact is the Yata Mirror even capable of being warped, as it is not a physical object. Going off this definition/image that Owarij showed in his first post:
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The answer would seem to be no. What I would find interesting is could the kamui "pierce through" or "ignore" the yata mirror and suck in whatever is being protected by it. It is stated that there is "no defense" against the technique. Could the Yata Mirror prevent whatever it's protecting from being sucked in to the other dimension? That would be what I would be interested in finding out.