Here are the scriptures in question:
"And it came to pass that when Coriantumr had leaned upon his sword, that he rested a little, he smote off the head of Shiz. And it came to pass that after he had smitten off the head of Shiz, that Shiz raised up on his hands and fell; and after that he had struggled for breath, he died." (Ether 15:30-31 )

According to Dr. M. Gary Hadfield, M.D., professor of pathology (neuropathology) at the Medical College of Virginia, Virginia Commonwealth University, in Richmond, Virginia:

"Shiz's death struggle illustrates the classic reflex posture that occurs in both humans and animals when the upper brain stem (midbrain/mesencephalon) is disconnected from the brain. The extensor muscles of the arms and legs contract, and this reflect action could cause Shiz to raise up on his hands."
(M. Gary Hadfield, "Neuropathy and the Scriptures," _BYU Studies_33/2 (1993): 312-20.)

It also depends on how complete the cut is and exactly where the cut is made. If the head was not completely severed from the body or if the cut is made high enough up the neck it is possible to leave part of the brain stem attached to the spinal cord, which could account for some movement. There are a number of historical reports that describe movements of a human body following beheading:

In 1336, King Ludwig of Bavaria sentenced nobleman Ditz von Shaunburg and four of his associates to death. The nobleman and his friends were to be beheaded. Before the execution, the king asked Ditz to express his final wish. The nobleman asked the king to forgive his friends if his beheaded body runs by them. Schaunburg specified that the convicted were supposed to get in a line with eight steps between each other. The king burst into laughter, but he promised to fulfill the nobleman-s last wish. Ditz got down on his knees in front of a block. The executioner cut his head off, but the body jumped up and ran by the other convicted people to the immense horror of the king and everyone who witnessed it. The beheaded body made 32 steps, having passed the last person in the line, tumbled down to the ground, and remained quiet. The king kept his promise.
(A beheaded body can take 32 steps - http://english.pravda.ru/main/2002/09/02/35725.html)

A soldier named Boris Luchkin was in an intelligence group during World War II. They had to cross the front line and go behind German lines. The commander of the group, a lieutenant, stepped on a mine. One of its fragments chopped his head off. Yet, the beheaded lieutenant remained standing, he unbuttoned his coat, took the map of their itinerary out, held it out to Luchnik, and then fell down on the grass. (In the magazine "Miracles and Adventures")

On the 17th of June, (1864?) in the charge of the Ninth Corps on the Confederate works east of Petersburg, a sergeant of the Fifty-Seventh Massachusetts leaped upon the parapet, and with his cap in his left hand and his musket in his right, stood cheering and gesturing with his arms to incite his comrades to come on. Suddenly a shell took off his head as completely as a knife could have done, but the tall form continued erect for some seconds, the arms still waving frantically but with ever-lessening sweep and power, until the forces of the body collapsed, when the headless trunk toppled over to the ground. (Popular Science Monthly, p.116 for June, 1892)

According to Alister Kershaw in "A History of the Guillotine":
"Beheading is effective and is probably as humane as any other modern method if carried out correctly. When a single blow is sufficient to decapitate the prisoner, they lose consciousness within a few seconds. Death occurs due to separation of the brain and spinal cord, after the transection (cutting through) of the surrounding tissues.
It has often been reported that the eyes and mouths of people beheaded have shown signs of movement. It has been calculated that the human brain has enough oxygen stored for metabolism to persist about seven seconds after the head is cut off. (Alister Kershaw "A History of the Guillotine")

A French physiologist named Pierre Jean Cabanis' was given the task in 1795 to determine if the victims of the guillotine were conscious after beheading The reason for the question was that after beheading the victims' bodies would often twitch. There were also tales of beheaded bodies standing up after the fall of the guillotine blade and walking around before finally collapsing.
It follows that a man who is guillotined suffers pain neither in his limbs nor in his head; that his death is as swift as the flow which strikes it; and if certain movements, whether regular or convulsive, are noticed in the muscles of the arms, legs, and face, they prove neither pain nor sensibility. They depend solely on a residue of the vital faculty which is not instantly abolished in the muscles and the nerves by death of the individual, the destruction of the self.
(Cabanis, Note sur le supplice de la guillotine (A Note on Execution by the Guillotine), Magasin encyclopédique, 1795, Oeurves complètes, 1823, Vol. 2, pp. 163-183, excerpted and translated by Solomon Diamond in Diamond, p. 39.)

Current and historical scientific studies and eyewitness reports confirm the possibility of movement of a body following beheading, as in the case of Shiz.