In the period of Oracle bone inscriptions (OBI) the Chinese word for ‘dying’ was written with a combination of 井 (a well, here meaning hole in the ground, grave) and a person centered in it. A different version turned up as a combination of bones 歹 and person 人. This one evolved into the modern character, except that in regular script (standing) person was replaced by fallen person 匕.²
Ochiai and Outlier take 死 as a semantic compound, which can be analyzed in any number of ways (a person who mourns the deceased, or the process whereby a person turns into a skeleton, etc.).³
Katō suggests a phonetic role for the element on the right, that seems to be based on identifying 人 or 匕 with 司. However, comparing the OBI shapes, that hypothesis seems highly unlikely (compare OBI for 死 with OBI for 司).⁴