Forget using "beheadings" against the Prophet, the Jewish Court of the Sanhedrin allows for "beheadings" (see Tractate Sanhedrin).
From the Tractate Sanhedrin:
The court had the power of inflicting four M. kinds of death penalty : stoning, burning, decapitation, and strangulation. R, Shimeon gives them in the order: 3 burning, stoning, strangulation, and decapitation. The regulations for those to be stoned have already been given. T. IX. 10. The court had the power of inflicting four kinds of death penalty, whereas the civil authority 4 can only inflict the penalty of the sword.
Mishna. VII. 3a. The regulations for those to be decapitated : their heads are cut off with a sword after the usage of the (Roman) Empire. R. Jehuda said : Such a death is too shameful ; on the contrary, a man's head is placed on the block and cut off with an axe. But it was replied : There is no death more shameful than this.
If anything the Prophet was following orders from the heavenly Court. Probably a case of "irony" on God's part, since Jewish tradition allowed for beheadings, that this was meted back to the unbelieving Jews.
The Quran excuses the death penalty for "charity".
Surah 4: 114 "And upon him who has slain a believer by mistake there is the duty of freeing a believing soul from bondage and paying an indemnity to the victim's relations,  unless they forgo it by way of charity."
Surah 5:45 (Asad) And We ordained for them in that [Torah]: A life for a life, and an eye for an eye, and a nose for a nose, and an ear for an ear, and a tooth for a tooth, and a [similar] retribution for wounds;  but he who shall forgo it out of charity will atone thereby for some of his past sins.  And they who do not judge in accordance with what God has revealed - they, they are the evildoers!
Charity nullifies the death penalty in the Quran. If only those devout Jihadists had even bothered to read the sacred texts perhaps then the world would be a bit more peaceful. Jihad was a temporary measure to preserve the life of the Prophet Muhammed and his believers since their lives were being threatened. A pledge had to be made to the Prophet Muhammed. If anyone even bothers to read the Quran, that is what you will find. It is not an internal struggle. It is not even something in force today. Fighting on God's behalf was also the instructions He gave to Israel with the destruction of certain tribes.
The Jews have been caught fighting in the Ukraine during it's uprising to preserve Jewish lives in the area. A former IDF solider in the Ukraine was using his fighting skills to push forward the revolution.
Still, many Jews supported the revolution and actively participated in it.
The fighting is probably gas, oil or banking related or a combination of all three.