The story
From Franco-American Novelty Company's brand name "Beagle Puss Disguise Kit", apparently from beagle + puss (“face”).
Etymology from Wiktionary, CC BY-SA 4.0.
beaglepuss
Today it means: A novelty pair of horn-rimmed glasses with attached eyebrows, plastic nose, and bushy mustache, caricaturing Groucho Marx. Full definition →