The eyes are not really different set of eyes but are a circuit (possibly similar to a
Magic Circuit) that opens up in the users brain and normal eyes,
[1] allowing them to "perceive death" in the form of lines and dots. The user in question is the only one who can touch or use these lines and dots (i.e. no one can interact with the lines/dots even if the user of the eyes were to point out their location on something).
These lines can then be traced with a sharp object such as a knife or a sword. Cutting the line “breaks” the object along that line and damage inflicted this way can not be healed or repaired in any way. Healing is possible if cutting the line doesn't completely separate a part of the object from the object itself.
[2] Also of note is how Arcueid was cut into a multitude of individual pieces as a result of having her lines traced but was able to survive anyway despite not being able to regenerate. She was able to accomplish this by completely reinventing the conceptual structure of her body, abandoning the conceptual structure that had been traced.
Dots can be pierced by sharp objects. Piercing a dot effectively “erases” that object from existence, in a sense that the object loses even its inherent properties such as momentum,
[3] toxicity,
[4] and generally any effect it may impose on it's surrounding.
[4][5][6][7] Living things whose dot was pierced get “stopped” and, as a consequence, die. While this
death may not be instant,
[8] it is absolutely permanent, and can't be reversed or bypassed, even by reincarnation.
Note that Tohno Shiki shows signs of mental/physical strain when using this ability extensively, manifested as headaches and even temporary loss of sight.
[9] Arcueid noted that this is due him having to “connect” to the perspective of an object he wishes to see the death of and that perceiving things in a way not meant for humans is putting a strain on his brain.
[10]
It is possible that Mystic Eyes of Death Perception are categorized as
Blue under the
Noble Colors system. Tohno Shiki's eyes glow with blue
[11], but this may be due to the color of Shiki's Jougan. It is also the dominant color of Ryougi Shiki's irises (see image) when her eyes are activated.