Green’s Dictionary of Slang

toss n.³

an act of dismissal.

1904

Ade ‘The Fable of [...] the Fearless Favorite from St. Louis’ in True Bills 66: He knew that he was taking a Chance, but an ordinary Toss had no Terrors for one accustomed to grappling with the Country Trade.

In phrases

give someone the toss (v.)

to dismiss, usu. from a job.

1902		Ade Breaking Into Society (1904) 152: He will wait until you begin to act real Friendly and then he will give you the Toss.
1970		J. Carroll ‘The Basketball Diaries’ in Paris Review Fall 107: I’ve lived here from time to time when my parents give me the toss and woke up here this morning, in fact, after a huge hash goof last night.

SE in slang uses

In phrases