In Soul Eater, Immortality is the apparent power which allows people to live forever. In addition, those with immortality are unable to die conventionally except in specific circumstances. In the world of Soul Eater, only select beings such as those within the Immortal Clan or gods like the Shinigami and the Great Old Ones truly possess the ability of Immortality.
Type 1 Immortality
Type 1 Immortality is a conjectural term used to describe the immortality that the Shinigami and the Great Old Ones possess due to being embodiment of Madness. In the case of the Full-fledged Shinigami and the Great Old Ones in the series, they're unable to die due to the fact that they embody madness.
Despite this, it seems only extremely powerful Death Scythes are capable of killing those with this sort of immortality. In the anime, the most powerful attack of the Great Traditional Techniques of the Scythe-Meister, the Kishin-Hunt (also known as the Kishin Hunter), is capable of overcoming this immortality.
Type 2 Immortality
Type 2 Immortality is a conjectural term used to describe the immortality that only the Immortal Clan and Free possess. This type of immortality not only allows the individual to survive any injuries, but also provides an extremely fast regenerating factor. It is still possible to kill an individual with this immortality type with either the use of the Great Traditional Techniques of the Scythe-Meister or (possibly) beheading.