According to Naruto wiki, a reanimated body can die from any of the following ways:
- Remove the soul from the reincarnated body, such as with the Dead Demon Consuming Seal.
Have the summoner end the technique. As they are unlikely to do this voluntarily, using a genjutsu to trick them into cancelling the technique is ideal.
A less reliable, though equally effective method is to have the reincarnated soul be affected in some emotional way that gives them closure, allowing their soul to break free of the Impure World Reincarnation's influence.
At episode 265, after Haku and Zabuza got reincarnated, they were faced by Kakashi and his army. At first, they were really hesitating to kill Kakashi and army and said that were under control of someone. Meanwhile, Kabuto used Mitarashi Anko to harness Orochimaru's chakra to tighten Haku's and Zabuza's soul to the body and as a result they became really powerful, a immortal killing puppet. They were fighting really hard and at episode 266(spoilers below):
How did they die? Neither of the above three points were followed i.e the soul were not removed by reaper death seal, nor the summoner was under a genjutsu nor the soul was affected in any emotional way. Yes, they were emotional at first but after getting Orochimaru's power, their soul were tightened more to the body which Kabuto felt that they were now a mere immortal killing machine.
Why did Zabuza and Haku got killed by a mere ninjustsu?