Kimi offers her dance to gain protection
the more she dances and performs, the harder to hurt her
but if someone give his/her offering more than Kimi does, he/she can hurt her
Futayo's offering is "as long as she is swinging her weapon then she can gain more speed"
when Futayo's offering matches Kimi's, she can hurt her
However, when Kimi asks her the question whihc is part of the performance (likes the singer asks her audience "Hey guy, are you entertained tonight?"),
Futayo fails hard hen she decides to use the slicing ability
At that moment, if Futayo can give more offering or answer her properly, she may break Kimi's defense
And about the slicing, I think most of the you get the idea already
so, may be Death note is useless against Kimi?