If a clean guillotine decapitation occurs, a few factors come into play. First, the blood vessels all vasoconstrict -- they'll close down, trapping oxygenated blood in the head. Also, neurological functions will start to shut off, reducing oxygen usage, in order to deal with the increasing hypoxia (this is also observed in drownings). As such, you can expect the head to "live" in various conditions for as much as a few minutes. You can expect consciousness for as much as 30 seconds and possibly more. Anectodotal reports of Guillotine (the doctor; not the device) come to us of experiments with convicted criminals who would answer YES with one eyeblink and NO with two blinks. The story goes that Guillotine ran out of questions before they stopped responding (over 2 minutes). Personally, I doubt this, but I don't know. On the other side of the equation is systemic shock. An injury like this would slam the patient into a (eventually terminal) shock. That, coupled with the hypoxia, indicates a super-fast loss of upper brain functions. So what one describes as "life" comes into question. As to the body, death would occur quickly, but would do so an organ at a time. Organ death depends a lot on which organ and how it's treated. You are no doubt aware that organs can be donated for quite some time post mortem.
jh
A mantis can live 1 day and a half without his head.
only a few seconds
5 years
1 second
Pubic lice can live less than a day without a human host.
im not not shure if you mean how long do cockroaches live without a head, but if so i read they can last about week.
Head lice live on the scalp, specifically close to the hair follicles where they can feed on blood several times a day. They do not wander far from the scalp as they cannot survive for long without a human host.
3 months
1 second
10 months in severe pain
46543563843 days. aprox.