https://www.reddit.com/r/AskHistorians/comments/5uyd6o/did_ordinary_people_in_roman_empire_shave/

There are a few threads on this that I was able to search. The above one should have some answers that could contribute. /u/Ben__edikt gives a good explanation.

The following page also links to some primary sources that discusses the treatment of beards in Roman times:

Men had not often the necessary implements for the various operations of the toilet; combs, mirrors, perfumes, and tools for clipping, cutting, shaving, &c. Accordingly the whole process had to be performed at the barber's, and hence the great concourse of people who daily gossiped at the tonstrina, or barber's shop. Besides the duties of a barber and hairdresser, strictly so called, the ancient tonsor discharged other offices. He was also a nail-parer. He was, in fact, much what the English barber was when he extracted teeth, as well as cut and dressed hair. People who kept the necessary instruments for all the different operations, generally had also slaves expressly for the purpose of performing them. The business of the barber was threefold. First there was the cutting of hair: hence the barber's question, πῶς σε κείρω (Plut. De Garrul. 13). For this purpose he used various knives of different sizes and shapes, and degrees of sharpness: hence Lucian (Adv. Indoct. c29), in enumerating the apparatus of a barber's shop, mentions πλῆθος μαχαιριδίων (μάχαιρα, μαχαιρίς, κουρίς are used also, in Latin culter); but scissors, ψαλίς, διπλῇ μάχαιρα (Pollux, II.32; in Latin forfex, axicia) were used too (compare Aristoph. Acharn. 848; Lucian, Pis. c46). Μάχαιρα was the usual word. Irregularity and unevenness of the hair was considered a great blemish, as appears generally, and from Horace (Sat. I.3.31, and Epist. I.1.94), and accordingly after the hair-cutting the uneven hairs were pulled out by tweezers, an operation to which Pollux (II.34) applies the term παραλέγεσθαι. So the hangers-on on great men, who wished to look young, were accustomed to pull out the grey hairs for them (Arist. Eq. 908).

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Barba.html