All credit goes to Thought Potato on YouTube and his video on Zombie Biology. TL;DR at the bottom but I would recommend reading the lot.
The Zombie virus or as he calls it, the Human Zombic Virus(HZV) is a zoonotic virus. It is from the order Mononegavirales(negative strand RNA viruses) along with Ebola, measles, and rabies. It spread to humans via ticks or tick bitten rats, raccoons, or other animals.
Once inside the victim, the virus quickly starts replicating inside the host’s cells. It utilizes a reverse transcriptase enzyme to produce DNA from its own RNA genome and then this DNA is put inside the host’s nucleus. Once inside the nucleus a integrase enzyme incorporates the DNA into the host’s genome; which essentially makes it a pro strand virus. This is very different from other Mononega virus because they do not produce DNA or use the nucleus for replication.
Quickly the victim will experience flu-like symptoms. Headaches, fever, and chills, alongside extreme thirst, itching, and increased heart rate and metabolism.
There are three stages that Thought Potato describes for HZV. The first stage is the symptoms described above with the victim quickly progressing to stage two.
Stage two is a coma that the victim falls into for four to six hours. During this time the fevers reach such a high level that the brain is damaged. Around midway through the coma the victim experiences cardiac arrest and the heart stops indefinitely. The victim’s blood flow, breathing, metabolism, and body temperature plummet, giving bystanders the impression that they have died(reason for why they come from graves and are called the living dead). They then enter stage three.
Stage three is when the real zombie appears. The victim, now zombie, rises in a catatonic state. Within an hour they start shambling around looking for flesh. Their heart may be stopped but their brain, though damaged, is still alive. This means that they remember parts of their lives and will try and return home. The brain is still working because of a barely functioning circulatory system. Organ failure and further brain damage remove the victim’s ability to reason, think, drive a car, or use tools. Certain hormones are still produced but serotonin production is almost immediately reduced. The smell of flesh flushes the victim’s brain with adrenaline-like neurotransmitters causing them to go into a frenzy.
Now to why they are still able to “live” with no beating heart. Following the cardiac arrest the nervous and circulatory systems are drastically restructured. The nervous system strengthens the pathways and innervating muscles. Skeletal muscles take up the role that the heart once had. They rhythmically contract and relax, pushing blood around. The blood becomes dark and viscous, filled with iron and bile. This increases oxygen levels but causes organs to fail. But because of the strengthened nervous system, the zombie is able to stay mobile much longer. This improved nervous system also allows for much greater regenerative abilities. Thought Potato states that a severed spinal cord is no problem and the zombie is able to walk again only 24 hours later. This is because of increased stem cell production and absence of obstructive glial scarring(scarring in the nervous system).
Other things are improved as well, such as smell, strength, and bite force. Sight rapidly decays along with hearing, touch, and the ability to feel pain.
Because of organ necrosis and the reduced ability to absorb nutrients from the meat they eat the zombie will die in less than a year.
TL;DR
Zombies can survive the failure of organs because of a strengthened nervous system. This nervous system allows them to stay mobile long after entire limbs have fallen off. The heart is stopped but blood continues flowing because skeletal muscles start rhythmically contracting and relaxing. The blood is dark and viscous because of increased iron and bile but oxygen levels are increased. The slow moving blood causes organs and muscles to experience necrosis and slowly die. Zombies do not last long without a good source and will die from starvation is only a few weeks. A zombie with food can live up to a year before their bodies literally fall apart.