This question was put to me again by a steel-string guitar owner, and I don’t blame the questioner. There are as many opinions on this as there are guitarists or guitars!!!
But shall we put this debate to rest, once and for all?
IT’S PERFECTLY SAFE TO CUT ALL THE STRINGS ON YOUR WESTERN FLAT-TOP (STEEL STRING) GUITAR AT ONE GO!
So, how did the doubt arise in the first place?
The Western flat-top guitar, as we know it, is a contemporary cousin of the Classical Guitar (Spanish Guitar), having evolved from it. The Classical Guitar – having its origins in the Lute and the Arabian Oud – acquired its final shape by the 1790s.
Classical and flamenco guitars historically used catgut strings, but these have been superseded by nylon. Catgut is a type of cord that is prepared from the natural fiber found in the walls of animal intestines. Catgut makers usually use sheep or goat intestines, but occasionally use the intestines of cattle, hogs, horses, mules, or donkeys. Despite the name, catgut is not made from cat intestines.
Classical Guitars were never constructed with a truss rod (which keeps the neck from bowing out of shape and gives relief to the neck) because the catgut strings never exerted as much tension as steel strings do. Ditto, nylon strings. And so, traditional wisdom said that while replacing strings on a Classical Guitar, strings should be replaced one at a time, to prevent the sudden loss in tension from misshaping the neck.
That knowledge continued to hold sway with the advent of Western Flat-top/Folk Guitars, even though they had a static steel rod or a truss rod in their necks to take the strain of the steel strings, and the same misinformation/lack of information keeps getting perpetuated by internet users even today.
So, to conclude, you can easily cut off all strings on a steel string guitar without fear of damaging the neck because it has a truss rod in it to maintain its shape. But one has to be careful while changing strings on a classical guitar.