Green’s Dictionary of Slang

1. (US) to mock, to laugh at.

1895		Philadelphia Inquirer (PA) 9 Sept. 7/6: ‘I gin der ole woman der grand laf [...] but she wuz dead game’.
1928		Sacramento Bee (CA) 28 Apr. 32/5: A lot of fresh kids stood around and give me the laugh.

2. (US) to dismiss; to terminate a relationship.

1904

C. Connors Bowery Life [ebook] ere's sum t'ings er bloke can't git out uv his nut fer er long time. Wun uv dem, is w'ere a bundle he is stuck on gives him de merry laugh—yer know, de t'row down, de dinky-dink.

(US campus) to humiliate, to make into a laughing-stock.

1911

E.B. Morris Junior 11: Moore. That bunch of Seniors mkes me weary. They are always trying to put the laugh on us.