You make a good point. The Rambam Avoda Zara 12:7 states "One is only Chayav if he shaves his beard with a razor; consequently, if one shaved with a scissors he is Patur". The general implication of such an expression would denote something that is forbidden.
In fact, the Kesef Mishna there notes this point but seems to consider it inconceivable that this was truly the Rambam's intent. Rather, he explains that this phraseology was used merely as a continuation of the language of the Mishna quoted previously that one is only Chayav on shaving with a razor, and he continued to use the same expression even though it is imprecise. Note that in the Shulchan Aruch Yoreh Deah 181:10 he uses the more precise term of "Muttar" (the Kesef Mishna was written by Rav Yosef Karo who also authored the Shulchan Aruch).
Also, the Gemara never actually says that a scissors is Pattur. What the Gemara Makkos 21a says is, "I might have thought that one who cuts his beard with a scissors is Chayav, had not the Torah written Lo Tashchis".
While one might question how the Kesef Mishna was so certain that the Rambam's intent was not consistent with his syntax; in fact, the previous Halacha in the Rambam makes this explanation an imperative. As in 12:6 he writes that it is Muttar to cut the Peyos with a scissors, and they are significantly more stringent than the beard. Most Poskim disagree with this Rambam and forbid cutting the Peyos completely with a scissors, it is inconceivable that the Rambam would permit Peyos while forbidding the beard.
While the Sefer HaChinuch 252 does understand the Rambam he way you cited him, he does not address the apparent contradiction to the previous Halacha. For more sources, see Darkei Teshuva 181§17 who quotes a number of Seforim who rule stringently on trimming the beard with a scissors; possibly some of them understand the Rambam this way. Also, look in the Mafteach of the Frankel Rambam on Avoda Zara 12:7 where he lists numerous Poskim who address this issue.