I think that beheading will be something that occurs often in the Tribulation for two reasons: first, while I do not agree with those who take the view that the Antichrist will come out of Islam (though I admit it is a possibility), I do think, seeing that the countries Prophecy speaks of being participants in the end days are all primarily Muslim, that this usual method of execution will be employed by them.
Secondly, it is a cheap means of execution and involves no technology, which is really the second point: technology will, due to the calamity involved, fail greatly in this period. The collapse of civilization is not something incredible that would take a great deal maneuvering to come about. Failure of the Power Systems would be enough to throw the entire world into chaos. Societies have become over-dependent on technology, and something as simple as the ability to store food could be enough to change the entire face of the earth.
But to answer the question more directly and bring the Antichrist into view, I don't think he will personally do the killing, but, in the atmosphere which arises in that Period, and when he sets himself up as a god, I see Scripture teaching that he will demand allegiance, and those who rebel against him will certainly be put to death.
I view the mark as a simple sign of allegiance to Antichrist, because again, I think technology will fail in general. And the one that controls the food in that day will be in control. If one cannot buy or sell without having the mark, and the means of obtaining the mark allegiance (which will actually be worship) to the Beast, this places those who trust in Christ in the position of either denying Christ and living physically, or dying as a consequence of the Beast's control over food.
Then we have those who I think will be sought out and demanded to come into allegiance. I think there will be a program where those who resist the Beast will be sought out and put to death for refusing to take the Mark.
God bless.