Green’s Dictionary of Slang

brand v.

(Scot. gang) to slash with a razor; thus to scar.

[UK](con. 1920s) McArthur & Long No Mean City 309: He slashed the blond girl across the lips, and his other weapon laid open the cheek of the nearest of her champions. The second young fellow hesitated for a fatal second and was ‘branded’ in turn.
[US]Goldin et al. DAUL 33/2: Brand, v. 1. To mark, as with a knife cut on the face.