According to Naruto.wikia.com/wiki/Kamui, this is the ability of Obito's right eye:
However, this eye can utilise a unique variation of teleportation akin to intangibility. When activated, any part of the user's body that overlaps with another object is seamlessly warped to Kamui's dimension, making it appear as though the user can phase through solid objects.
So if one part of Obito's body, let's say a part of his head (like in this picture below), was separated from the rest of his body, shouldn't he be dead? His left eye and the left side of his face is in the Kamui dimension, while the rest of his body is in the normal dimension (Earth).