My theory is that Kakashi only warped the tail and this is why.
If Kakashi can all of a sudden warp entire tailed beast then why miss one tail?
..... What actually happened is similar to how killer bee survived from Sasuke Amaterasu.
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For those that don't know how Bee got away from Sasuke.....
A tail was cut by Sasuke's lightning technique and this tailed cut allows Bee to escape but minus one tail. The remaining Eight tails that gets hit by Sasuke Amaterasu is just a one tail substitute (If you apply this to 610 then you might agree with what I am saying.)
Therefore, the reason a tail was cut in 610 is so that Kakashi can warp the eight tails minus one tail which is shown in the final panel of 610. In addition, the one tail you see in front of the nine tails is the substitute.
This is just my opinion but I am pretty sure we will find out what officially happened in the next manga release