Green’s Dictionary of Slang

in prize-fighting and elsewhere, a blow that knocks down its recipient.

1851		Bell’s Life in Sydney 11 Jan. 2/1: Bullock-skin did it, administering a neat grasser, which dyed the turf a most brilliant crimson.
1857		Bell’s Life in Victoria (Melbourne) 25 July 2/3: [of foxhunting] On rising, both [horses] swerved against Wizard, and knocked him clean over, giving his rider a complete grasser.