The foundational question turns on what instrument the Torah forbids: Vayikra 19:27 prohibits destroying the corner of the beard, and the Gemara (Makkot 21a) resolves the apparent tension between the two verbs — 'shave' and 'destroy' — by ruling that only shaving that constitutes destruction is biblically forbidden, and that this uniquely describes the razor (תער), not scissors.
This talmudic principle is carried forward through the rishonim and codifiers: the Tur (Yoreh De'ah 181) records the Rambam's view that scissors even cut close as a razor are permitted, while noting the Rosh's stricter position that scissors still incur liability for the corners of the head; the Beit Yosef (Yoreh De'ah 181) explains that the Mishnah's phrase 'he is not liable' implies outright permission, not merely exemption from lashes, citing the Tosefta as direct support; and the Shulchan Arukh (Yoreh De'ah 181:3) rules accordingly that one is liable only through a razor, though he registers the view of those who forbid scissors that shave like a razor, adding that this opinion deserves consideration.
The Rema and later Acharonim refine the scissors discussion further: the Rema (Yoreh De'ah 181:3) cautions that when trimming with scissors one should use the upper blade rather than the lower, lest the lower blade function alone as a razor, and the Levush (Yoreh De'ah 181:10) explains the underlying concern — that if the upper jaw does not cut, the lower jaw alone functions exactly like a razor.
The Sdei Chemed (Maarechet Gimel 75) surveys earlier responsa on whether scissors not close as a razor are at minimum permitted, while also recording the opinion of the Tzemach Tzedek that even scissors not close as a razor may be forbidden, and that beyond the cutting prohibition there is a concern of violating the prohibition against a man adorning himself in a woman's manner — indicating that this question drew stringent opinions going beyond the purely technical cutting analysis.
Turning to the modern responsa on the actual device: the Minchas Yitzchak (4:113) addresses a halachic inquiry from a God-fearing merchant asking whether he may sell a new design of electric shaving machine to observant Jews, and, on our reading of the cited page, analyzes the physical mechanism — a perforated metal screen with internal rotating blades — to determine whether it constitutes forbidden razor-shaving or permitted scissor-like cutting, focusing on how close the internal blade approaches the skin.
The Shevet HaLevi (5:100) is not available in full text for Mekoros to read, but our reading of the cited page indicates that he addresses the minimum length of hair that must remain when trimming the beard so as not to violate the prohibitions of hashchatah, and examines the opinions of the Rambam, Rosh, and Smag on what constitutes a halachically sufficient remnant.