c. 1200, from Late Latin Saxonem (nominative Saxo; also source of French Saxon, Spanish Sajon, Italian Sassone), usually found in plural Saxones, probably from a West Germanic tribal name (represented by Old English Seaxe, Old High German Sahsun, German Sachse "Saxon"), traditionally regarded as meaning literally "warrior with knives" (compare Old English seax, Old Frisian, Old Norse sax "knife, short sword, dagger," Old High German Saxnot, name of a war-god), from Proto-Germanic *sahsa- "knife," from PIE root *sek- "to cut." But Watkins considers this doubtful.
The word figures in the well-known story, related by Geoffrey of Monmouth, who got it from Nennius, of the treacherous slaughter by the Anglo-Saxons of their British hosts:
Accordingly they all met at the time and place appointed, and began to treat of peace; and when a fit opportunity offered for executing his villany, Hengist cried out, "Nemet oure Saxas," and the same instant seized Vortigern, and held him by his cloak. The Saxons, upon the signal given, drew their daggers, and falling upon the princes, who little suspected any such design, assassinated them to the number of four hundred and sixty barons and consuls ....
The OED editors helpfully point out that the correct Old English (with an uninflected plural) would be nimað eowre seax. For other Germanic national names that may have derived from characteristic tribal weapons, see Frank, Lombard. As an adjective from 1560s. Still in 20c. used by Celtic speakers to mean "an Englishman" (Welsh Sais, plural Seison "an Englishman;" Seisoneg "English").
In reference to the modern German state of Saxony (German Sachsen, French Saxe) it is attested from 1630s. Saxon is the source of the -sex in Essex, Sussex, etc. (compare Middlesex, from Old English Middel-Seaxe "Middle Saxons"). Bede distinguished the Anglo-Saxons, who conquered much of southern Britain, from the Ealdesaxe "Old Saxons," who stayed in Germany.