I found a weakness, Theoretically it might work. I got this bit from a article about the doll on the wiki
"Perhaps one of the Tails Doll's most notable qualities is the gem from atop its head. Referred to as the Blood Gem for the dim, red, blood-like glow, it seems to be the Tails Doll's power source, a "heart" of sorts. It seems to contain the souls of the victims it has slain over the years. If one manages to severe it from the stem, the Tails Doll will either weaken or die. However, death is not permanent for the Tails Doll, as unless slain by the Pure Souls, the Tails Doll will simply restore itself a few moments later, using the soul of one of the victims stored to replenish itself." The end said it would use the soul of a victim. so in theory if you cut the gem from the stem enough you can end it forever.