Going by the databook this is basically the unstoppable force vs the immoveable object.
This is what kamui says;
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Ill pick out the most important parts. Firstly its an s/t technique. Basically its a form of ninjutsu albeit it doujutsu (eye techniques). Secondly it says and i quote "There is no technique that can compete against this one"
The yata mirror;
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Ill pick out the most important parts. Firstly it has no physical form because its a spiritual weapon, but alot of people get confused by this. It turns from a spiritual weapon with no substance to a material weapon, no different to the totsuka sword which comes from the sake jar. Both are ethereal weapons, but they then turn material when needed. Either to pierce or cut an opponent this is in relation to the totsuka sword or to defend from bombs or attacks, this is in relation to the yata mirror. The question is in its material form can kamui take advantage over this. I dont believe so because it says "in the face of a god power, all attacks, whether from a material or astra body, ninjutsu or physical lose their meaning, Kumai falls under this.
Secondly it goes on to say it alters its properties in accordance with the attributes of the attack, rendering the attack ineffective. One of the way it can do this to kamui is if it goes back to its ethereal (spiritual) state