Baxter first attracted notice in 1879 when he established the weekly comic periodical Comus (afterwards altered to Momus,) published in Manchester. He specialized in comic portraits and drew a series of nearly life-sized heads called “Studies from Dickens” for that paper. When Momus failed in 1883 he moved to London where with a friend and brother artist he designed political and humorous Christmas cards. Baxter began contributing to Judy; or, the London Serio-Comic Journal, under Charles Henry Ross, but really came to prominence on Ally Sloper’s Half-Holiday published by Gilbert Dalziel. Baxter breathed new life into CHR’s creation Ally Sloper with his large, masterly full-page cover illustrations and double-page interior spreads. Later he seceded from that journal and in conjunction with C. H. Ross, creator of Sloper, he started Choodle, which had a short life due to a breakdown in the artist’s health.
Like Ross he was an amateur actor. He died at age 32 on 2 June 1888 of ‘rapid consumption.’ In August 1888 Gilbert Dalziel issued from 99 Shoe-lane “Fifty Sloper Cartoons,” for a shilling, as a souvenir of the late artist. In June 1889 Baxter’s work was exhibited at the Royal Institute, Picadilly “Works of English Humourists.” The show had only a few works by Hogarth but devoted an entire gallery to the work of Thomas Rowlandson. Also featured were works by Cruikshank, Leech, Phiz, Seymour, Furniss, Tenniel, Sambourne, Keane, Fred Barnard, Charles Green, and Du Maurier. At the same time Cassell’s put on a black and white exhibition of magazine illustrators at the Memorial Hall on Farrington-street.